1. IMPORT ALL LIBRARIES¶

In [ ]:
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
from statsmodels.tsa.seasonal import seasonal_decompose
from statsmodels.tsa.stattools import adfuller
from sklearn.metrics import mean_absolute_error, r2_score
from sklearn.ensemble import RandomForestRegressor
from sklearn.preprocessing import StandardScaler
import warnings
warnings.filterwarnings("ignore")

2. LOAD THE DATASET¶

In [ ]:
data = pd.read_excel('../Data/Bidru Awana Final.xlsx')
data.head()
Out[ ]:
Year Station Day Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
0 1995 Bidru Awana 1.0 0.235 0.223 0.223 0.248 0.331 0.26 0.260 0.547 0.413 0.362 0.109 0.082
1 1995 Bidru Awana 2.0 0.235 0.223 0.223 0.248 0.331 0.301 0.260 4.351 0.59 0.331 0.109 0.082
2 1995 Bidru Awana 3.0 0.235 0.223 0.223 0.223 0.301 0.274 0.248 1.516 0.683 0.316 0.109 0.082
3 1995 Bidru Awana 4.0 0.235 0.223 0.223 0.212 0.301 0.26 0.248 1.436 2.582 0.301 0.109 0.082
4 1995 Bidru Awana 5.0 0.235 0.223 0.223 0.212 1.683 0.26 0.248 2.152 3.193 0.301 0.101 0.082
In [ ]:
# List of stations to keep
stations_to_keep = ["Mean", "Flow (MCM)", "Maximum", "Minimum", "Runoff (mm)"]
# Filter the dataframe
filtered_df = data[data["Station "].isin(stations_to_keep)]
filtered_df.tail()
Out[ ]:
Year Station Day Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
967 2021 Mean NaN 0.703 0.415 0.415 0.725 0.260 0.324 1.789 1.770 0.549 0.384 0.246 0.197
968 2021 Flow (MCM) NaN 1.884 1.112 1.112 1.879 0.696 0.84 4.793 4.741 1.423 1.027 0.637 0.526
969 2021 Maximum NaN 0.842 0.508 0.508 1.033 0.858 4.483 9.308 8.756 2.34 1.127 0.281 0.255
970 2021 Minimum NaN 0.501 0.326 0.326 0.484 0.095 0.109 0.177 0.368 0.323 0.243 0.209 0.177
971 2021 Runoff (mm) NaN 3.582 2.114 2.114 3.572 1.972 2.479 6.897 11.641 4.716 5.058 5.533 2.838
In [ ]:
filtered_df.rename(columns={'Station ':'Parameter'}, inplace=True)
filtered_df.drop(columns={'Day'}, inplace=True)
filtered_df.head()
Out[ ]:
Year Parameter Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
31 1995 Mean 0.224 0.223 0.227 0.309 0.341 0.289 0.437 0.788 1 0.159 0.096 0.075
32 1995 Flow (MCM) 0.601 0.539 0.609 0.802 0.914 0.749 1.171 2.112 2.591 0.426 0.25 0.201
33 1995 Maximum 0.235 0.223 0.260 0.569 1.683 0.59 0.838 2.351 2.217 0.362 0.109 0.082
34 1995 Minimum 0.212 0.223 0.212 0.2 0.235 0.248 0.248 0.346 0.316 0.109 0.082 0.070
35 1995 Runoff (mm) 1.658 1.158 1.861 1.554 2.298 1.266 2.556 1.507 2.198 1.387 1.088 2.893

3. TRANSFORM THE DATASET¶

In [ ]:
# Remove extra spaces
filtered_df.columns = filtered_df.columns.str.strip()
filtered_df.head()
Out[ ]:
Year Parameter Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
31 1995 Mean 0.224 0.223 0.227 0.309 0.341 0.289 0.437 0.788 1 0.159 0.096 0.075
32 1995 Flow (MCM) 0.601 0.539 0.609 0.802 0.914 0.749 1.171 2.112 2.591 0.426 0.25 0.201
33 1995 Maximum 0.235 0.223 0.260 0.569 1.683 0.59 0.838 2.351 2.217 0.362 0.109 0.082
34 1995 Minimum 0.212 0.223 0.212 0.2 0.235 0.248 0.248 0.346 0.316 0.109 0.082 0.070
35 1995 Runoff (mm) 1.658 1.158 1.861 1.554 2.298 1.266 2.556 1.507 2.198 1.387 1.088 2.893
In [ ]:
filtered_df.columns
Out[ ]:
Index(['Year', 'Parameter', 'Jan', 'Feb', 'Mar', 'Apr', 'May', 'Jun', 'Jul',
       'Aug', 'Sep', 'Oct', 'Nov', 'Dec'],
      dtype='object')
In [ ]:
def transform_data(df):
    # Melt the dataframe
    melted_df = df.melt(id_vars=["Parameter", "Year"],
                        value_vars=["Jan", "Feb", "Mar", "Apr", "May", "Jun", "Jul", "Aug", "Sep", "Oct", "Nov", "Dec"],
                        var_name="Month", value_name="Value")

    # Map month names to numbers
    month_mapping = {
        "Jan": "01", "Feb": "02", "Mar": "03", "Apr": "04", "May": "05", "Jun": "06",
        "Jul": "07", "Aug": "08", "Sep": "09", "Oct": "10", "Nov": "11", "Dec": "12"
    }
    melted_df["Month"] = melted_df["Month"].map(month_mapping)

    # Combine Year and Month into a Date column
    melted_df["Date"] = pd.to_datetime(melted_df["Year"].astype(str) + "-" + melted_df["Month"] + "-01")

    # Select and reorder the final columns
    transformed_df = melted_df[["Parameter", "Date", "Value"]]

    return transformed_df
In [ ]:
# Transform the data
transformed_data = transform_data(filtered_df)
In [ ]:
transformed_data.head()
Out[ ]:
Parameter Date Value
0 Mean 1995-01-01 0.224
1 Flow (MCM) 1995-01-01 0.601
2 Maximum 1995-01-01 0.235
3 Minimum 1995-01-01 0.212
4 Runoff (mm) 1995-01-01 1.658
In [ ]:
# UNIQUE VALUES ONLY
unique_parameters = transformed_data['Parameter'].unique()
In [ ]:
for index, row in transformed_data.iterrows():
    value = row['Value']
    if not isinstance(value, (int, float)):
        print(f"Index: {index}, Date: {row['Date']}, Value: {value}")
In [ ]:
transformed_data.Value.isnull().sum()
Out[ ]:
0
In [ ]:
# Convert 'Value' column to float
transformed_data['Value'] = transformed_data['Value'].astype(float)
In [ ]:
# RENAMA THE PARAMETERS
rename_dict = {
    unique_parameters[0]: 'Mean Flow',
    unique_parameters[1]: 'FLow',
    unique_parameters[2]: 'Max FLow',
    unique_parameters[3]: 'Min Flow',
    unique_parameters[4]: 'Runoff'
}

# Renaming the parameters
transformed_data['Parameter'] = transformed_data['Parameter'].replace(rename_dict)
transformed_data.head()
Out[ ]:
Parameter Date Value
0 Mean Flow 1995-01-01 0.224
1 FLow 1995-01-01 0.601
2 Max FLow 1995-01-01 0.235
3 Min Flow 1995-01-01 0.212
4 Runoff 1995-01-01 1.658
In [ ]:
# Parameter counts
transformed_data.Parameter.value_counts()
Out[ ]:
Parameter
Mean Flow    324
FLow         324
Max FLow     324
Min Flow     324
Runoff       324
Name: count, dtype: int64

4. PLOT VALUES OF EACH PARAMETERS¶

In [ ]:
parameters = transformed_data['Parameter'].unique()

custom_colors = {
    parameters[0]: '#2ca02c',
    parameters[1]: '#8b0000',
    parameters[2]: '#ff6347',
    parameters[3]: '#8c564b',
    parameters[4]: '#ff7f0e',
}

plt.figure(figsize=(40, 10))

for parameter in parameters:
    parameter_data = transformed_data[transformed_data['Parameter'] == parameter]
    parameter_data.set_index('Date', inplace=True)
    sns.lineplot(data=parameter_data,
                 x=parameter_data.index,
                 y='Value',
                 marker='o',
                 label=parameter,
                 linewidth=1,
                 color=custom_colors[parameter])

# plt.title('Monthly Analysis', fontsize=24)
plt.xlabel('Date', fontsize=24)
plt.ylabel('Streamflow(m3/s)', fontsize=26)
plt.legend(loc='best', fontsize=24, framealpha=0.5)
plt.xticks(fontsize=24)
plt.yticks(fontsize=24)
plt.show()
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In [ ]:
parameters = transformed_data['Parameter'].unique()

custom_colors = {
    # parameters[0]: '#2ca02c',
    # parameters[1]: '#8b0000',
    parameters[2]: '#ff6347',
    parameters[3]: '#8c564b',
    # parameters[4]: '#ff7f0e',
}

plt.figure(figsize=(40, 20))

for parameter in parameters[2:4]:
    parameter_data = transformed_data[transformed_data['Parameter'] == parameter]
    parameter_data.set_index('Date', inplace=True)
    sns.lineplot(data=parameter_data,
                 x=parameter_data.index,
                 y='Value',
                 marker='o',
                 label=parameter,
                 linewidth=1,
                 color=custom_colors[parameter])

# plt.title('Monthly Analysis', fontsize=24)
plt.xlabel('Date', fontsize=24)
plt.ylabel('Streamflow(m3/s)', fontsize=26)
plt.legend(loc='best', fontsize=24, framealpha=0.5)
plt.xticks(fontsize=24)
plt.yticks(fontsize=24)
plt.show()
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In [ ]:
parameters = transformed_data['Parameter'].unique()
parameters
Out[ ]:
array(['Mean Flow', 'FLow', 'Max FLow', 'Min Flow', 'Runoff'],
      dtype=object)

5. FIND THE CORRELATIONS BETWEEN EACH PARAMETERS¶

In [ ]:
transformed_data = transformed_data.drop_duplicates(subset=['Date', 'Parameter'])

# Pivot the data
pivot_data = transformed_data.pivot(index='Date', columns='Parameter', values='Value')

# Calculate the correlation matrix
correlation_matrix = pivot_data.corr()

# Plot the heatmap
plt.figure(figsize=(16, 10))
sns.heatmap(correlation_matrix, annot=True, cmap='coolwarm', square=True, linewidths=0.5, annot_kws={"size": 18})

# Adjust x-tick and y-tick labels rotation
plt.xticks(rotation=90, fontsize=20)
plt.yticks(rotation=0, fontsize=20)

plt.xlabel('')
plt.ylabel('')
plt.show()
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6. COMMON FUNCTION¶

TIME SERIES TO SUPERVISED¶

In [ ]:
def series_to_supervised(data, n_in=1, n_out=1, dropnan=True):
    n_vars = 1 if type(data) is list else data.shape[1]
    df = pd.DataFrame(data)
    cols = []
    for i in range(n_in, 0, -1):
        cols.append(df.shift(i))
    for i in range(0, n_out):
        cols.append(df.shift(-i))
    agg = pd.concat(cols, axis=1)
    if dropnan:
        agg.dropna(inplace=True)
    return agg.values

ADD ROLLING FEATURES¶

In [ ]:
def add_rolling_features(data, window=3):
    df = pd.DataFrame(data)
    df['rolling_mean'] = df.iloc[:, 0].rolling(window=window).mean()
    df['rolling_std'] = df.iloc[:, 0].rolling(window=window).std()
    df.dropna(inplace=True)
    return df

TRAIN TEST SPLITT¶

In [ ]:
def train_test_split(data, train_size=0.9):
    n_train = int(len(data) * train_size)
    return data[:n_train], data[n_train:]

MEASURING METRICS¶

In [ ]:
def nash_sutcliffe_efficiency(y_true, y_pred):
    return 1 - (np.sum((y_true - y_pred)**2) / np.sum((y_true - np.mean(y_true))**2))
def willmotts_index(y_true, y_pred):
    return 1 - (np.sum((y_pred - y_true)**2) / np.sum((np.abs(y_pred - np.mean(y_true)) + np.abs(y_true - np.mean(y_true)))**2))

CROSS VALIDATION AND MODEL EVALUATIONS¶

In [ ]:
def walk_forward_validation(data, model):
    predictions = []
    train, test = train_test_split(data)
    history = [x for x in train.values]
    for i in range(len(test)):
        testX, testy = test.iloc[i, :-1].values, test.iloc[i, -1]
        yhat = model(history, testX)
        predictions.append(yhat)
        history.append(test.iloc[i].values)
        print('>expected=%.1f, predicted=%.1f' % (testy, yhat))
    mae = mean_absolute_error(test.iloc[:, -1], predictions)
    rmse = np.sqrt(np.mean((test.iloc[:, -1] - np.asarray(predictions))**2))
    r2 = r2_score(test.iloc[:, -1], predictions)
    nse = nash_sutcliffe_efficiency(test.iloc[:, -1], predictions)
    willmott = willmotts_index(test.iloc[:, -1], predictions)
    return mae, rmse, r2, nse, willmott, test.index, test.iloc[:, -1], predictions

7. MODELS¶

1. RANDOM FOREST¶

In [ ]:
def random_forest_forecast(train, testX):
    train = np.asarray(train)
    trainX, trainy = train[:, :-1], train[:, -1]
    model = RandomForestRegressor(n_estimators=50)
    model.fit(trainX, trainy)
    yhat = model.predict([testX])
    return yhat[0]

2. SVM¶

In [ ]:
from sklearn.svm import SVR
def svm_forecast(train, testX):
    train = np.asarray(train)
    trainX, trainy = train[:, :-1], train[:, -1]
    model = SVR(kernel='rbf')
    model.fit(trainX, trainy)
    yhat = model.predict([testX])
    return yhat[0]

3. XGBRegressor¶

In [ ]:
from xgboost import XGBRegressor
def xgboost_forecast(train, testX):
    train = np.asarray(train)
    trainX, trainy = train[:, :-1], train[:, -1]
    model = XGBRegressor(n_estimators=50)
    model.fit(trainX, trainy)
    yhat = model.predict([testX])
    return yhat[0]

4. LGBMRegressor¶

In [ ]:
from lightgbm import LGBMRegressor
def lightgbm_forecast(train, testX):
    train = np.asarray(train)
    trainX, trainy = train[:, :-1], train[:, -1]
    model = LGBMRegressor(n_estimators=50, verbose=-1)
    model.fit(trainX, trainy)
    yhat = model.predict([testX])
    return yhat[0]
In [ ]:
# Color dictionary for different models
colors_dict = {
    'LightGBM': '#27ad81',
    'XGBoost': '#5dc863',
    'SVM': '#aadc32',
    'Random Forest': '#fde725'
}

6. MEAN FLOW ANALYSIS¶

In [ ]:
# Get the mean flow values
mean_flow = transformed_data[transformed_data['Parameter'] == parameters[0]]
mean_flow.head()
Out[ ]:
Parameter Date Value
0 Mean Flow 1995-01-01 0.224000
5 Mean Flow 1996-01-01 0.163161
10 Mean Flow 1997-01-01 0.181000
15 Mean Flow 1998-01-01 0.295000
20 Mean Flow 1999-01-01 0.144000
In [ ]:
# drop the parameter columns
mean_flow = mean_flow.drop(columns=['Parameter'])
In [ ]:
mean_flow.head()
Out[ ]:
Date Value
0 1995-01-01 0.224000
5 1996-01-01 0.163161
10 1997-01-01 0.181000
15 1998-01-01 0.295000
20 1999-01-01 0.144000
In [ ]:
# sort according to  the date
mean_flow= mean_flow.sort_values(by='Date')
mean_flow.head()
Out[ ]:
Date Value
0 1995-01-01 0.224
135 1995-02-01 0.223
270 1995-03-01 0.227
405 1995-04-01 0.309
540 1995-05-01 0.341
In [ ]:
mean_flow.head()
Out[ ]:
Date Value
0 1995-01-01 0.224
135 1995-02-01 0.223
270 1995-03-01 0.227
405 1995-04-01 0.309
540 1995-05-01 0.341
In [ ]:
# Find the row with the maximum value
max_value_row = mean_flow.loc[mean_flow['Value'].idxmax()]

# Print the date with the maximum value
print(f"Date with the maximum value: {mean_flow['Date']}")
print(f"Maximum value: {max_value_row['Value']}")

Date with the maximum value: 0      1995-01-01
135    1995-02-01
270    1995-03-01
405    1995-04-01
540    1995-05-01
          ...    
1075   2021-08-01
1210   2021-09-01
1345   2021-10-01
1480   2021-11-01
1615   2021-12-01
Name: Date, Length: 324, dtype: datetime64[ns]
Maximum value: 2.829
In [ ]:
plt.figure(figsize=(20, 8))
mean_flow.plot(x='Date', y='Value', kind='line', ax=plt.gca(), color='#2ca02c', fontsize=12)
plt.xlabel('Date', fontdict={'fontsize':20})
plt.ylabel('Mean Flow (m3/s)', fontdict={'fontsize':20})
plt.xticks(size = 20)
plt.yticks(size = 20)
plt.grid(linestyle='--')
plt.tight_layout()
plt.legend().remove()
plt.show()
No description has been provided for this image
In [ ]:
# Add fuller test to check the stationarity of the dataset
def adfuller_test(values):
    result = adfuller(values)
    labels = ['ADF Test Statistic','p-value','#Lags Used', 'Number of Observations Used']
    for value, label in zip(result, labels):
        print(label+' : '+str(value))
    if result[1] <= 0.05:
        print("Strong evidence against the null hypothesis(H0)")
    else:
        print("Weak evidence against the null hypothesis(H0)")
In [ ]:
# H0: It is non stationary
# H1: It is stationary
In [ ]:
adfuller_test(mean_flow['Value'])

ADF Test Statistic : -2.4945372082496937
p-value : 0.11680914517324759
#Lags Used : 13
Number of Observations Used : 310
Weak evidence against the null hypothesis(H0)
In [ ]:
mean_flow = mean_flow[['Date', 'Value']]
mean_flow.set_index('Date', inplace=True)
mean_flow.head()
Out[ ]:
Value
Date
1995-01-01 0.224
1995-02-01 0.223
1995-03-01 0.227
1995-04-01 0.309
1995-05-01 0.341
In [ ]:
model_names = []
mae_values = []
rmse_values = []
r2_values = []
nse_values = []
willmott_values = []

TRAIN THE MODEL¶

In [ ]:
# Assuming `mean flow` is your time series DataFrame
series = mean_flow
values = series.values
values = add_rolling_features(values, window=3)
values = pd.DataFrame(values).values
scaler = StandardScaler()
values = scaler.fit_transform(values)
data = series_to_supervised(values, n_in=6)
data_df = pd.DataFrame(data, index=series.index[6+2:])
In [ ]:
# Model names
models = [
    ('LightGBM', lightgbm_forecast),
    ('XGBoost', xgboost_forecast),
    ('SVM', svm_forecast),
    ('Random Forest', random_forest_forecast)
]

# Clear existing lists in case they contain previous values
model_names.clear()
mae_values.clear()
rmse_values.clear()
r2_values.clear()
nse_values.clear()
willmott_values.clear()

# Iterate over each model, perform walk-forward validation, and append metrics to lists
for model_name, model_func in models:
    mae, rmse, r2, nse, willmott, test_index, y, yhat = walk_forward_validation(data_df, model_func)
    
    model_names.append(model_name)
    mae_values.append(mae)
    rmse_values.append(rmse)
    r2_values.append(r2)
    nse_values.append(nse)
    willmott_values.append(willmott)

# Create a DataFrame
metrics = {
    'Model': model_names,
    'MAE': mae_values,
    'RMSE': rmse_values,
    'R-squared': r2_values,
    'Nash-Sutcliffe Efficiency': nse_values,
    'Willmott\'s Index of Agreement': willmott_values
}

metrics_df = pd.DataFrame(metrics)

# Plot the actual vs predicted values for each model
plt.figure(figsize=(16, 6))
plt.plot(test_index, y, label='Actual', linestyle='--', color='black', linewidth=2)


# Plot predictions for each model
for model_name, model_func in models:
    _, _, _, _, _, test_index, _, yhat = walk_forward_validation(data_df, model_func)
    plt.plot(test_index, yhat, label=f'{model_name} Predicted', linestyle='--', color=colors_dict[model_name], linewidth=2)

plt.xlabel('Year and Month', fontsize=18)
plt.ylabel('Scaled Mean Flow(m3/s)', fontsize=18)
plt.legend(fontsize=14, loc='upper center', bbox_to_anchor=(0.6, 1.15), ncol=1)
plt.xticks(rotation=45, fontsize=14)
plt.yticks(fontsize=14)

plt.grid(axis='y', linestyle='--')

ax = plt.gca()
ax.spines['top'].set_visible(False)
ax.spines['right'].set_visible(False)

plt.tight_layout()
plt.show()

>expected=-0.7, predicted=-0.6
>expected=-0.4, predicted=-0.5
>expected=-0.2, predicted=0.0
>expected=3.4, predicted=1.9
>expected=3.2, predicted=2.0
>expected=3.6, predicted=2.0
>expected=-0.0, predicted=-0.0
>expected=-0.7, predicted=-0.5
>expected=-0.6, predicted=-0.8
>expected=-0.7, predicted=-0.7
>expected=-0.8, predicted=-0.7
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=0.0, predicted=-0.2
>expected=1.9, predicted=1.6
>expected=1.1, predicted=2.5
>expected=0.2, predicted=1.6
>expected=1.3, predicted=0.6
>expected=1.4, predicted=0.7
>expected=-0.8, predicted=-0.8
>expected=0.5, predicted=-0.0
>expected=0.4, predicted=-0.0
>expected=-0.2, predicted=0.4
>expected=-0.2, predicted=0.0
>expected=0.0, predicted=-0.2
>expected=0.1, predicted=0.0
>expected=2.2, predicted=1.9
>expected=2.1, predicted=2.3
>expected=1.7, predicted=1.9
>expected=1.8, predicted=1.8
>expected=-0.3, predicted=-0.3
>expected=-0.5, predicted=-0.5
>expected=-0.7, predicted=-0.7
>expected=-0.4, predicted=-0.3
>expected=-0.2, predicted=-0.2
>expected=3.4, predicted=3.1
>expected=3.2, predicted=2.0
>expected=3.6, predicted=2.2
>expected=-0.0, predicted=-0.1
>expected=-0.7, predicted=-0.6
>expected=-0.6, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.8, predicted=-0.7
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=0.0, predicted=-0.2
>expected=1.9, predicted=1.6
>expected=1.1, predicted=2.2
>expected=0.2, predicted=1.6
>expected=1.3, predicted=0.7
>expected=1.4, predicted=0.9
>expected=-0.8, predicted=-0.8
>expected=0.5, predicted=0.2
>expected=0.4, predicted=-0.0
>expected=-0.2, predicted=0.1
>expected=-0.2, predicted=0.1
>expected=0.0, predicted=-0.1
>expected=0.1, predicted=0.2
>expected=2.2, predicted=2.2
>expected=2.1, predicted=2.0
>expected=1.7, predicted=1.9
>expected=1.8, predicted=1.8
>expected=-0.3, predicted=-0.3
>expected=-0.5, predicted=-0.5
>expected=-0.7, predicted=-0.6
>expected=-0.4, predicted=-0.4
>expected=-0.2, predicted=-0.1
>expected=3.4, predicted=2.9
>expected=3.2, predicted=2.4
>expected=3.6, predicted=2.6
>expected=-0.0, predicted=0.4
>expected=-0.7, predicted=-0.0
>expected=-0.6, predicted=-0.4
>expected=-0.7, predicted=-0.4
>expected=-0.8, predicted=-0.5
>expected=-0.8, predicted=-0.5
>expected=-0.8, predicted=-0.8
>expected=0.0, predicted=-0.2
>expected=1.9, predicted=1.9
>expected=1.1, predicted=1.5
>expected=0.2, predicted=0.7
>expected=1.3, predicted=1.1
>expected=1.4, predicted=1.0
>expected=-0.8, predicted=-0.6
>expected=0.5, predicted=-0.5
>expected=0.4, predicted=-0.3
>expected=-0.2, predicted=0.2
>expected=-0.2, predicted=0.2
>expected=0.0, predicted=-0.1
>expected=0.1, predicted=0.1
>expected=2.2, predicted=1.3
>expected=2.1, predicted=1.8
>expected=1.7, predicted=2.0
>expected=1.8, predicted=1.8
>expected=-0.3, predicted=-0.2
>expected=-0.5, predicted=-0.6
>expected=-0.7, predicted=-0.6
>expected=-0.4, predicted=-0.4
>expected=-0.2, predicted=-0.2
>expected=3.4, predicted=2.2
>expected=3.2, predicted=1.8
>expected=3.6, predicted=2.4
>expected=-0.0, predicted=-0.0
>expected=-0.7, predicted=-0.6
>expected=-0.6, predicted=-0.6
>expected=-0.7, predicted=-0.7
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=0.0, predicted=-0.2
>expected=1.9, predicted=1.3
>expected=1.1, predicted=2.4
>expected=0.2, predicted=1.2
>expected=1.3, predicted=0.6
>expected=1.4, predicted=0.7
>expected=-0.8, predicted=-0.8
>expected=0.5, predicted=-0.2
>expected=0.4, predicted=-0.3
>expected=-0.2, predicted=0.5
>expected=-0.2, predicted=0.2
>expected=0.0, predicted=0.0
>expected=0.1, predicted=0.1
>expected=2.2, predicted=1.7
>expected=2.1, predicted=2.1
>expected=1.7, predicted=1.7
>expected=1.8, predicted=1.8
>expected=-0.3, predicted=-0.2
>expected=-0.5, predicted=-0.5
>expected=-0.7, predicted=-0.6
>expected=-0.4, predicted=-0.5
>expected=-0.2, predicted=0.0
>expected=3.4, predicted=1.9
>expected=3.2, predicted=2.0
>expected=3.6, predicted=2.0
>expected=-0.0, predicted=-0.0
>expected=-0.7, predicted=-0.5
>expected=-0.6, predicted=-0.8
>expected=-0.7, predicted=-0.7
>expected=-0.8, predicted=-0.7
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=0.0, predicted=-0.2
>expected=1.9, predicted=1.6
>expected=1.1, predicted=2.5
>expected=0.2, predicted=1.6
>expected=1.3, predicted=0.6
>expected=1.4, predicted=0.7
>expected=-0.8, predicted=-0.8
>expected=0.5, predicted=-0.0
>expected=0.4, predicted=-0.0
>expected=-0.2, predicted=0.4
>expected=-0.2, predicted=0.0
>expected=0.0, predicted=-0.2
>expected=0.1, predicted=0.0
>expected=2.2, predicted=1.9
>expected=2.1, predicted=2.3
>expected=1.7, predicted=1.9
>expected=1.8, predicted=1.8
>expected=-0.3, predicted=-0.3
>expected=-0.5, predicted=-0.5
>expected=-0.7, predicted=-0.7
>expected=-0.4, predicted=-0.3
>expected=-0.2, predicted=-0.2
>expected=3.4, predicted=3.1
>expected=3.2, predicted=2.0
>expected=3.6, predicted=2.2
>expected=-0.0, predicted=-0.1
>expected=-0.7, predicted=-0.6
>expected=-0.6, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.8, predicted=-0.7
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=0.0, predicted=-0.2
>expected=1.9, predicted=1.6
>expected=1.1, predicted=2.2
>expected=0.2, predicted=1.6
>expected=1.3, predicted=0.7
>expected=1.4, predicted=0.9
>expected=-0.8, predicted=-0.8
>expected=0.5, predicted=0.2
>expected=0.4, predicted=-0.0
>expected=-0.2, predicted=0.1
>expected=-0.2, predicted=0.1
>expected=0.0, predicted=-0.1
>expected=0.1, predicted=0.2
>expected=2.2, predicted=2.2
>expected=2.1, predicted=2.0
>expected=1.7, predicted=1.9
>expected=1.8, predicted=1.8
>expected=-0.3, predicted=-0.3
>expected=-0.5, predicted=-0.5
>expected=-0.7, predicted=-0.6
>expected=-0.4, predicted=-0.4
>expected=-0.2, predicted=-0.1
>expected=3.4, predicted=2.9
>expected=3.2, predicted=2.4
>expected=3.6, predicted=2.6
>expected=-0.0, predicted=0.4
>expected=-0.7, predicted=-0.0
>expected=-0.6, predicted=-0.4
>expected=-0.7, predicted=-0.4
>expected=-0.8, predicted=-0.5
>expected=-0.8, predicted=-0.5
>expected=-0.8, predicted=-0.8
>expected=0.0, predicted=-0.2
>expected=1.9, predicted=1.9
>expected=1.1, predicted=1.5
>expected=0.2, predicted=0.7
>expected=1.3, predicted=1.1
>expected=1.4, predicted=1.0
>expected=-0.8, predicted=-0.6
>expected=0.5, predicted=-0.5
>expected=0.4, predicted=-0.3
>expected=-0.2, predicted=0.2
>expected=-0.2, predicted=0.2
>expected=0.0, predicted=-0.1
>expected=0.1, predicted=0.1
>expected=2.2, predicted=1.3
>expected=2.1, predicted=1.8
>expected=1.7, predicted=2.0
>expected=1.8, predicted=1.8
>expected=-0.3, predicted=-0.2
>expected=-0.5, predicted=-0.6
>expected=-0.7, predicted=-0.6
>expected=-0.4, predicted=-0.4
>expected=-0.2, predicted=-0.2
>expected=3.4, predicted=2.2
>expected=3.2, predicted=1.8
>expected=3.6, predicted=2.4
>expected=-0.0, predicted=-0.1
>expected=-0.7, predicted=-0.6
>expected=-0.6, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.8, predicted=-0.7
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=0.0, predicted=-0.3
>expected=1.9, predicted=1.6
>expected=1.1, predicted=2.2
>expected=0.2, predicted=1.4
>expected=1.3, predicted=0.7
>expected=1.4, predicted=0.7
>expected=-0.8, predicted=-0.8
>expected=0.5, predicted=-0.1
>expected=0.4, predicted=-0.3
>expected=-0.2, predicted=0.4
>expected=-0.2, predicted=0.2
>expected=0.0, predicted=0.2
>expected=0.1, predicted=0.2
>expected=2.2, predicted=1.2
>expected=2.1, predicted=2.0
>expected=1.7, predicted=1.7
>expected=1.8, predicted=1.7
>expected=-0.3, predicted=-0.2
>expected=-0.5, predicted=-0.4
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EVALUATE THE MODEL¶

In [ ]:
# Create a DataFrame
metrics = {
    'Model': model_names,
    'MAE': mae_values,
    'RMSE': rmse_values,
    'R-squared': r2_values,
    'Nash-Sutcliffe Efficiency': nse_values,
    'Willmott\'s Index of Agreement': willmott_values
}

metrics = pd.DataFrame(metrics)
In [ ]:
metrics
Out[ ]:
Model MAE RMSE R-squared Nash-Sutcliffe Efficiency Willmott's Index of Agreement
0 LightGBM 0.403790 0.629322 0.768773 0.768773 0.927839
1 XGBoost 0.302683 0.502463 0.852598 0.852598 0.957353
2 SVM 0.343343 0.446910 0.883390 0.883390 0.964259
3 Random Forest 0.380600 0.584901 0.800263 0.800263 0.937047
In [ ]:
metrics = metrics.round(2)
fig, ax = plt.subplots(figsize=(20, 4))
ax.axis('off')

table = ax.table(cellText=metrics.values,
                 colLabels=metrics.columns,
                 cellLoc='center',
                 loc='center',
                 bbox=[0, 0, 1, 1])

table.auto_set_font_size(False)
table.set_fontsize(10)
table.scale(1.2, 1.2)

header_color = '#D0D0D0'
data_color = '#FFFFFF'

for i, key in enumerate(table._cells):
    cell = table._cells[key]
    cell.set_edgecolor('black')
    if key[0] == 0 or key[1] == -1:
        cell.set_text_props(weight='bold')
        cell.set_facecolor(header_color)
    else:
        cell.set_facecolor(data_color)

plt.title('Models Performance on Mean Flow')
plt.show()
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In [ ]:
colors = ['#27ad81', '#5dc863', '#aadc32', '#fde725']
bar_width = 0.4

# Metrics and Titles
metrics_title = {
    'MAE': 'Mean Absolute Error (MAE)',
    'RMSE': 'Root Mean Squared Error (RMSE)',
    'R-squared': 'R-squared',
    'Nash-Sutcliffe Efficiency': 'Nash-Sutcliffe Efficiency',
    'Willmott\'s Index of Agreement': 'Willmott\'s Index of Agreement'
}

# Plot each metric separately
for metric, title in metrics_title.items():
    fig, ax = plt.subplots(figsize=(8, 6))
    ax.bar(metrics['Model'], metrics[metric], color=colors, width=bar_width)
    # ax.set_title(title, fontsize=16)
    ax.set_ylabel(metric, fontsize=16)
    ax.tick_params(axis='x', rotation=30, labelsize=16)
    ax.tick_params(axis='y', labelsize=16)
    plt.tight_layout()
    plt.show()
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7. FLOW ANALYSIS¶

In [ ]:
# Get the temp_max values
flow = transformed_data[transformed_data['Parameter'] == parameters[1]]
flow.head()
Out[ ]:
Parameter Date Value
1 FLow 1995-01-01 0.60100
6 FLow 1996-01-01 4.89483
11 FLow 1997-01-01 0.48600
16 FLow 1998-01-01 0.79000
21 FLow 1999-01-01 0.38500
In [ ]:
# drop the parameter columns
flow = flow.drop(columns=['Parameter'])
In [ ]:
flow.head()
Out[ ]:
Date Value
1 1995-01-01 0.60100
6 1996-01-01 4.89483
11 1997-01-01 0.48600
16 1998-01-01 0.79000
21 1999-01-01 0.38500
In [ ]:
# sort according to  the date
flow= flow.sort_values(by='Date')
flow.head()
Out[ ]:
Date Value
1 1995-01-01 0.601
136 1995-02-01 0.539
271 1995-03-01 0.609
406 1995-04-01 0.802
541 1995-05-01 0.914
In [ ]:
flow.head()
Out[ ]:
Date Value
1 1995-01-01 0.601
136 1995-02-01 0.539
271 1995-03-01 0.609
406 1995-04-01 0.802
541 1995-05-01 0.914
In [ ]:
plt.figure(figsize=(20, 8))
flow.plot(x='Date', y='Value', kind='line', ax=plt.gca(), color='#8b0000', fontsize=12)
plt.xlabel('Date', fontdict={'fontsize':20})
plt.ylabel('Flow (m3/s)', fontdict={'fontsize':20})
plt.xticks(size = 20)
plt.yticks(size = 20)
plt.grid(linestyle='--')
plt.tight_layout()
plt.legend().remove()
plt.show()
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In [ ]:
# Add fuller test to check the stationarity of the dataset
def adfuller_test(values):
    result = adfuller(values)
    labels = ['ADF Test Statistic','p-value','#Lags Used', 'Number of Observations Used']
    for value, label in zip(result, labels):
        print(label+' : '+str(value))
    if result[1] <= 0.05:
        print("Strong evidence against the null hypothesis(H0)")
    else:
        print("Weak evidence against the null hypothesis(H0)")
In [ ]:
# H0: It is non stationary
# H1: It is stationary
In [ ]:
adfuller_test(flow['Value'])

ADF Test Statistic : -2.592225967325901
p-value : 0.09461467042325716
#Lags Used : 13
Number of Observations Used : 310
Weak evidence against the null hypothesis(H0)
In [ ]:
flow = flow[['Date', 'Value']]
flow.set_index('Date', inplace=True)
flow.head()
Out[ ]:
Value
Date
1995-01-01 0.601
1995-02-01 0.539
1995-03-01 0.609
1995-04-01 0.802
1995-05-01 0.914
In [ ]:
flow_model_names = []
flow_mae_values = []
flow_rmse_values = []
flow_r2_values = []
flow_nse_values = []
flow_willmott_values = []

TRAIN THE MODELS¶

In [ ]:
# Assuming `temp_max` is your time series DataFrame
series = flow
values = series.values
values = add_rolling_features(values, window=3)
values = pd.DataFrame(values).values
scaler = StandardScaler()
values = scaler.fit_transform(values)
data = series_to_supervised(values, n_in=6)
data_df = pd.DataFrame(data, index=series.index[6+2:])
In [ ]:
# Model names
models = [
    ('LightGBM', lightgbm_forecast),
    ('XGBoost', xgboost_forecast),
    ('SVM', svm_forecast),
    ('Random Forest', random_forest_forecast)
]

# Clear existing lists in case they contain previous values
model_names.clear()
mae_values.clear()
rmse_values.clear()
r2_values.clear()
nse_values.clear()
willmott_values.clear()

# Iterate over each model, perform walk-forward validation, and append metrics to lists
for model_name, model_func in models:
    mae, rmse, r2, nse, willmott, test_index, y, yhat = walk_forward_validation(data_df, model_func)
    
    model_names.append(model_name)
    mae_values.append(mae)
    rmse_values.append(rmse)
    r2_values.append(r2)
    nse_values.append(nse)
    willmott_values.append(willmott)

# Create a DataFrame
metrics = {
    'Model': model_names,
    'MAE': mae_values,
    'RMSE': rmse_values,
    'R-squared': r2_values,
    'Nash-Sutcliffe Efficiency': nse_values,
    'Willmott\'s Index of Agreement': willmott_values
}

metrics_df = pd.DataFrame(metrics)

# Plot the actual vs predicted values for each model
plt.figure(figsize=(16, 6))
plt.plot(test_index, y, label='Actual', linestyle='--', color='black', linewidth=2)



for model_name, model_func in models:
    _, _, _, _, _, test_index, _, yhat = walk_forward_validation(data_df, model_func)
    plt.plot(test_index, yhat, label=f'{model_name} Predicted', linestyle='--', color=colors_dict[model_name], linewidth=2)

plt.xlabel('Year and Month', fontsize=18)
plt.ylabel('Scaled Flow (m3/s)', fontsize=18)

plt.legend(fontsize=14, loc='upper right', bbox_to_anchor=(0.6, 1.15), ncol=1)

plt.xticks(rotation=45, fontsize=14)
plt.yticks(fontsize=14)

plt.grid(axis='y', linestyle='--')

ax = plt.gca()
ax.spines['top'].set_visible(False)
ax.spines['right'].set_visible(False)

plt.tight_layout()
plt.show()

>expected=-0.7, predicted=-0.6
>expected=-0.4, predicted=-0.6
>expected=-0.2, predicted=0.0
>expected=3.4, predicted=2.0
>expected=3.2, predicted=1.7
>expected=3.6, predicted=1.9
>expected=-0.1, predicted=-0.1
>expected=-0.7, predicted=-0.6
>expected=-0.6, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.0, predicted=-0.2
>expected=1.9, predicted=2.0
>expected=1.1, predicted=2.6
>expected=0.2, predicted=1.8
>expected=1.2, predicted=0.7
>expected=1.4, predicted=0.7
>expected=-0.8, predicted=-0.7
>expected=0.5, predicted=0.0
>expected=0.4, predicted=-0.0
>expected=-0.3, predicted=0.4
>expected=-0.3, predicted=-0.2
>expected=-0.0, predicted=-0.2
>expected=0.0, predicted=0.1
>expected=2.2, predicted=1.8
>expected=2.2, predicted=2.0
>expected=1.7, predicted=1.9
>expected=1.9, predicted=1.7
>expected=-0.3, predicted=-0.1
>expected=-0.5, predicted=-0.6
>expected=-0.7, predicted=-0.7
>expected=-0.4, predicted=-0.5
>expected=-0.2, predicted=-0.1
>expected=3.4, predicted=2.0
>expected=3.2, predicted=1.9
>expected=3.6, predicted=2.8
>expected=-0.1, predicted=0.0
>expected=-0.7, predicted=-0.6
>expected=-0.6, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.0, predicted=-0.2
>expected=1.9, predicted=1.7
>expected=1.1, predicted=1.7
>expected=0.2, predicted=0.9
>expected=1.2, predicted=0.6
>expected=1.4, predicted=0.8
>expected=-0.8, predicted=-0.8
>expected=0.5, predicted=0.1
>expected=0.4, predicted=-0.2
>expected=-0.3, predicted=0.2
>expected=-0.3, predicted=-0.1
>expected=-0.0, predicted=-0.2
>expected=0.0, predicted=-0.2
>expected=2.2, predicted=1.5
>expected=2.2, predicted=2.2
>expected=1.7, predicted=1.7
>expected=1.9, predicted=1.9
>expected=-0.3, predicted=-0.3
>expected=-0.5, predicted=-0.5
>expected=-0.7, predicted=-0.7
>expected=-0.4, predicted=-0.5
>expected=-0.2, predicted=-0.1
>expected=3.4, predicted=2.9
>expected=3.2, predicted=2.4
>expected=3.6, predicted=2.4
>expected=-0.1, predicted=0.3
>expected=-0.7, predicted=-0.0
>expected=-0.6, predicted=-0.4
>expected=-0.7, predicted=-0.4
>expected=-0.8, predicted=-0.5
>expected=-0.8, predicted=-0.5
>expected=-0.8, predicted=-0.8
>expected=-0.0, predicted=-0.2
>expected=1.9, predicted=2.0
>expected=1.1, predicted=1.5
>expected=0.2, predicted=0.8
>expected=1.2, predicted=1.0
>expected=1.4, predicted=0.9
>expected=-0.8, predicted=-0.6
>expected=0.5, predicted=-0.5
>expected=0.4, predicted=0.0
>expected=-0.3, predicted=0.4
>expected=-0.3, predicted=0.2
>expected=-0.0, predicted=-0.2
>expected=0.0, predicted=0.1
>expected=2.2, predicted=1.4
>expected=2.2, predicted=1.5
>expected=1.7, predicted=1.8
>expected=1.9, predicted=1.6
>expected=-0.3, predicted=-0.3
>expected=-0.5, predicted=-0.6
>expected=-0.7, predicted=-0.6
>expected=-0.4, predicted=-0.4
>expected=-0.2, predicted=-0.1
>expected=3.4, predicted=2.0
>expected=3.2, predicted=1.9
>expected=3.6, predicted=2.3
>expected=-0.1, predicted=-0.1
>expected=-0.7, predicted=-0.6
>expected=-0.6, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.0, predicted=-0.3
>expected=1.9, predicted=1.9
>expected=1.1, predicted=1.7
>expected=0.2, predicted=1.0
>expected=1.2, predicted=0.6
>expected=1.4, predicted=0.8
>expected=-0.8, predicted=-0.8
>expected=0.5, predicted=-0.2
>expected=0.4, predicted=-0.3
>expected=-0.3, predicted=0.4
>expected=-0.3, predicted=0.3
>expected=-0.0, predicted=0.0
>expected=0.0, predicted=0.1
>expected=2.2, predicted=1.5
>expected=2.2, predicted=1.9
>expected=1.7, predicted=1.8
>expected=1.9, predicted=1.7
>expected=-0.3, predicted=-0.3
>expected=-0.5, predicted=-0.5
>expected=-0.7, predicted=-0.6
>expected=-0.4, predicted=-0.6
>expected=-0.2, predicted=0.0
>expected=3.4, predicted=2.0
>expected=3.2, predicted=1.7
>expected=3.6, predicted=1.9
>expected=-0.1, predicted=-0.1
>expected=-0.7, predicted=-0.6
>expected=-0.6, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.0, predicted=-0.2
>expected=1.9, predicted=2.0
>expected=1.1, predicted=2.6
>expected=0.2, predicted=1.8
>expected=1.2, predicted=0.7
>expected=1.4, predicted=0.7
>expected=-0.8, predicted=-0.7
>expected=0.5, predicted=0.0
>expected=0.4, predicted=-0.0
>expected=-0.3, predicted=0.4
>expected=-0.3, predicted=-0.2
>expected=-0.0, predicted=-0.2
>expected=0.0, predicted=0.1
>expected=2.2, predicted=1.8
>expected=2.2, predicted=2.0
>expected=1.7, predicted=1.9
>expected=1.9, predicted=1.7
>expected=-0.3, predicted=-0.1
>expected=-0.5, predicted=-0.6
>expected=-0.7, predicted=-0.7
>expected=-0.4, predicted=-0.5
>expected=-0.2, predicted=-0.1
>expected=3.4, predicted=2.0
>expected=3.2, predicted=1.9
>expected=3.6, predicted=2.8
>expected=-0.1, predicted=0.0
>expected=-0.7, predicted=-0.6
>expected=-0.6, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.0, predicted=-0.2
>expected=1.9, predicted=1.7
>expected=1.1, predicted=1.7
>expected=0.2, predicted=0.9
>expected=1.2, predicted=0.6
>expected=1.4, predicted=0.8
>expected=-0.8, predicted=-0.8
>expected=0.5, predicted=0.1
>expected=0.4, predicted=-0.2
>expected=-0.3, predicted=0.2
>expected=-0.3, predicted=-0.1
>expected=-0.0, predicted=-0.2
>expected=0.0, predicted=-0.2
>expected=2.2, predicted=1.5
>expected=2.2, predicted=2.2
>expected=1.7, predicted=1.7
>expected=1.9, predicted=1.9
>expected=-0.3, predicted=-0.3
>expected=-0.5, predicted=-0.5
>expected=-0.7, predicted=-0.7
>expected=-0.4, predicted=-0.5
>expected=-0.2, predicted=-0.1
>expected=3.4, predicted=2.9
>expected=3.2, predicted=2.4
>expected=3.6, predicted=2.4
>expected=-0.1, predicted=0.3
>expected=-0.7, predicted=-0.0
>expected=-0.6, predicted=-0.4
>expected=-0.7, predicted=-0.4
>expected=-0.8, predicted=-0.5
>expected=-0.8, predicted=-0.5
>expected=-0.8, predicted=-0.8
>expected=-0.0, predicted=-0.2
>expected=1.9, predicted=2.0
>expected=1.1, predicted=1.5
>expected=0.2, predicted=0.8
>expected=1.2, predicted=1.0
>expected=1.4, predicted=0.9
>expected=-0.8, predicted=-0.6
>expected=0.5, predicted=-0.5
>expected=0.4, predicted=0.0
>expected=-0.3, predicted=0.4
>expected=-0.3, predicted=0.2
>expected=-0.0, predicted=-0.2
>expected=0.0, predicted=0.1
>expected=2.2, predicted=1.4
>expected=2.2, predicted=1.5
>expected=1.7, predicted=1.8
>expected=1.9, predicted=1.6
>expected=-0.3, predicted=-0.3
>expected=-0.5, predicted=-0.6
>expected=-0.7, predicted=-0.6
>expected=-0.4, predicted=-0.4
>expected=-0.2, predicted=-0.1
>expected=3.4, predicted=2.0
>expected=3.2, predicted=1.9
>expected=3.6, predicted=2.1
>expected=-0.1, predicted=-0.2
>expected=-0.7, predicted=-0.6
>expected=-0.6, predicted=-0.6
>expected=-0.7, predicted=-0.7
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.0, predicted=-0.3
>expected=1.9, predicted=1.9
>expected=1.1, predicted=1.9
>expected=0.2, predicted=1.2
>expected=1.2, predicted=0.5
>expected=1.4, predicted=0.8
>expected=-0.8, predicted=-0.8
>expected=0.5, predicted=-0.2
>expected=0.4, predicted=-0.2
>expected=-0.3, predicted=0.4
>expected=-0.3, predicted=0.2
>expected=-0.0, predicted=0.2
>expected=0.0, predicted=0.1
>expected=2.2, predicted=1.5
>expected=2.2, predicted=1.9
>expected=1.7, predicted=1.8
>expected=1.9, predicted=1.6
>expected=-0.3, predicted=-0.2
>expected=-0.5, predicted=-0.5
No description has been provided for this image

EVALUATE THE MODEL¶

In [ ]:
# Create a DataFrame
metrics = {
    'Model': model_names,
    'MAE': mae_values,
    'RMSE': rmse_values,
    'R-squared': r2_values,
    'Nash-Sutcliffe Efficiency': nse_values,
    'Willmott\'s Index of Agreement': willmott_values
}

metrics = pd.DataFrame(metrics)
In [ ]:
metrics
Out[ ]:
Model MAE RMSE R-squared Nash-Sutcliffe Efficiency Willmott's Index of Agreement
0 LightGBM 0.409872 0.660180 0.751504 0.751504 0.921768
1 XGBoost 0.308311 0.478650 0.869374 0.869374 0.959671
2 SVM 0.366457 0.478225 0.869605 0.869605 0.958244
3 Random Forest 0.359409 0.548506 0.828463 0.828463 0.944408
In [ ]:
metrics = metrics.round(2)

fig, ax = plt.subplots(figsize=(20, 4))
ax.axis('off')

table = ax.table(cellText=metrics.values,
                 colLabels=metrics.columns,
                 cellLoc='center',
                 loc='center',
                 bbox=[0, 0, 1, 1])

table.auto_set_font_size(False)
table.set_fontsize(10)
table.scale(1.2, 1.2)

header_color = '#D0D0D0'
data_color = '#FFFFFF'

for i, key in enumerate(table._cells):
    cell = table._cells[key]
    cell.set_edgecolor('black')
    if key[0] == 0 or key[1] == -1:
        cell.set_text_props(weight='bold')
        cell.set_facecolor(header_color)
    else:
        cell.set_facecolor(data_color)

plt.title('Models Performance on Flow')
plt.show()
No description has been provided for this image
In [ ]:
colors = ['#27ad81', '#5dc863', '#aadc32', '#fde725']
bar_width = 0.4

# Metrics and Titles
metrics_title = {
    'MAE': 'Mean Absolute Error (MAE)',
    'RMSE': 'Root Mean Squared Error (RMSE)',
    'R-squared': 'R-squared',
    'Nash-Sutcliffe Efficiency': 'Nash-Sutcliffe Efficiency',
    'Willmott\'s Index of Agreement': 'Willmott\'s Index of Agreement'
}

# Plot each metric separately
for metric, title in metrics_title.items():
    fig, ax = plt.subplots(figsize=(8, 6))
    ax.bar(metrics['Model'], metrics[metric], color=colors, width=bar_width)
    # ax.set_title(title, fontsize=16)
    ax.set_ylabel(metric, fontsize=16)
    ax.tick_params(axis='x', rotation=30, labelsize=16)
    ax.tick_params(axis='y', labelsize=16)
    plt.tight_layout()
    plt.show()
No description has been provided for this image
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8. MAX FLOW ANALYSIS¶

In [ ]:
# Get the temp_max values
flow_max = transformed_data[transformed_data['Parameter'] == parameters[2]]
flow_max.head()
Out[ ]:
Parameter Date Value
2 Max FLow 1995-01-01 0.235
7 Max FLow 1996-01-01 0.345
12 Max FLow 1997-01-01 0.223
17 Max FLow 1998-01-01 0.362
22 Max FLow 1999-01-01 0.159
In [ ]:
# drop the parameter columns
flow_max = flow_max.drop(columns=['Parameter'])
In [ ]:
flow_max.head()
Out[ ]:
Date Value
2 1995-01-01 0.235
7 1996-01-01 0.345
12 1997-01-01 0.223
17 1998-01-01 0.362
22 1999-01-01 0.159
In [ ]:
# sort according to  the date
flow_max= flow_max.sort_values(by='Date')
flow_max.head()
Out[ ]:
Date Value
2 1995-01-01 0.235
137 1995-02-01 0.223
272 1995-03-01 0.260
407 1995-04-01 0.569
542 1995-05-01 1.683
In [ ]:
flow_max.head()
Out[ ]:
Date Value
2 1995-01-01 0.235
137 1995-02-01 0.223
272 1995-03-01 0.260
407 1995-04-01 0.569
542 1995-05-01 1.683
In [ ]:
plt.figure(figsize=(20, 8))
flow_max.plot(x='Date', y='Value', kind='line', ax=plt.gca(), color='#ff6347', fontsize=12)
plt.xlabel('Date', fontdict={'fontsize':20})
plt.ylabel('Max Flow (m3/s)', fontdict={'fontsize':20})
plt.xticks(size = 20)
plt.yticks(size = 20)
plt.grid(linestyle='--')
plt.tight_layout()
plt.legend().remove()
plt.show()
No description has been provided for this image
In [ ]:
# Add fuller test to check the stationarity of the dataset
def adfuller_test(values):
    result = adfuller(values)
    labels = ['ADF Test Statistic','p-value','#Lags Used', 'Number of Observations Used']
    for value, label in zip(result, labels):
        print(label+' : '+str(value))
    if result[1] <= 0.05:
        print("Strong evidence against the null hypothesis(H0)")
    else:
        print("Weak evidence against the null hypothesis(H0)")
In [ ]:
# H0: It is non stationary
# H1: It is stationary
In [ ]:
adfuller_test(flow_max['Value'])

ADF Test Statistic : -4.083392870423538
p-value : 0.001031585994254914
#Lags Used : 13
Number of Observations Used : 310
Strong evidence against the null hypothesis(H0)
In [ ]:
flow_max = flow_max[['Date', 'Value']]
flow_max.set_index('Date', inplace=True)
flow_max.head()
Out[ ]:
Value
Date
1995-01-01 0.235
1995-02-01 0.223
1995-03-01 0.260
1995-04-01 0.569
1995-05-01 1.683
In [ ]:
flow_max_model_names = []
flow_max_mae_values = []
flow_max_rmse_values = []
flow_max_r2_values = []
flow_max_nse_values = []
flow_max_willmott_values = []

TRAIN THE MODEL¶

In [ ]:
# Assuming `flow_max` is your time series DataFrame
series = flow_max
values = series.values
values = add_rolling_features(values, window=3)
values = pd.DataFrame(values).values
scaler = StandardScaler()
values = scaler.fit_transform(values)
data = series_to_supervised(values, n_in=6)
data_df = pd.DataFrame(data, index=series.index[6+2:])
In [ ]:
# Model names
models = [
    ('LightGBM', lightgbm_forecast),
    ('XGBoost', xgboost_forecast),
    ('SVM', svm_forecast),
    ('Random Forest', random_forest_forecast)
]

# Clear existing lists in case they contain previous values
model_names.clear()
mae_values.clear()
rmse_values.clear()
r2_values.clear()
nse_values.clear()
willmott_values.clear()

# Iterate over each model, perform walk-forward validation, and append metrics to lists
for model_name, model_func in models:
    mae, rmse, r2, nse, willmott, test_index, y, yhat = walk_forward_validation(data_df, model_func)
    
    model_names.append(model_name)
    mae_values.append(mae)
    rmse_values.append(rmse)
    r2_values.append(r2)
    nse_values.append(nse)
    willmott_values.append(willmott)

# Create a DataFrame
metrics = {
    'Model': model_names,
    'MAE': mae_values,
    'RMSE': rmse_values,
    'R-squared': r2_values,
    'Nash-Sutcliffe Efficiency': nse_values,
    'Willmott\'s Index of Agreement': willmott_values
}

metrics_df = pd.DataFrame(metrics)

# Plot the actual vs predicted values for each model
plt.figure(figsize=(16, 6))
plt.plot(test_index, y, label='Actual', linestyle='--', color='black', linewidth=2)

for model_name, model_func in models:
    _, _, _, _, _, test_index, _, yhat = walk_forward_validation(data_df, model_func)
    plt.plot(test_index, yhat, label=f'{model_name} Predicted', linestyle='--', color=colors_dict[model_name], linewidth=2)

plt.xlabel('Year and Month', fontsize=18)
plt.ylabel('Scaled Max Flow (m3/s)', fontsize=18)

plt.legend(fontsize=14, loc='upper right', bbox_to_anchor=(0.6, 1.15), ncol=1)

plt.xticks(rotation=45, fontsize=14)
plt.yticks(fontsize=14)
plt.grid(axis='y', linestyle='--')
ax = plt.gca()
ax.spines['top'].set_visible(False)
ax.spines['right'].set_visible(False)

plt.tight_layout()
plt.show()

>expected=-0.6, predicted=-0.6
>expected=-0.5, predicted=-0.5
>expected=-0.5, predicted=-0.4
>expected=3.0, predicted=2.3
>expected=2.9, predicted=2.7
>expected=3.0, predicted=2.7
>expected=-0.2, predicted=0.1
>expected=-0.6, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.2, predicted=-0.3
>expected=-0.2, predicted=-0.2
>expected=-0.5, predicted=-0.3
>expected=-0.5, predicted=-0.5
>expected=-0.2, predicted=-0.3
>expected=-0.1, predicted=-0.1
>expected=-0.7, predicted=-0.6
>expected=-0.5, predicted=-0.6
>expected=-0.5, predicted=-0.6
>expected=-0.6, predicted=-0.5
>expected=-0.6, predicted=-0.5
>expected=-0.6, predicted=-0.4
>expected=0.1, predicted=0.1
>expected=0.9, predicted=0.6
>expected=0.3, predicted=1.2
>expected=0.7, predicted=1.4
>expected=0.8, predicted=0.9
>expected=-0.3, predicted=-0.4
>expected=-0.5, predicted=-0.5
>expected=-0.6, predicted=-0.6
>expected=-0.5, predicted=-0.5
>expected=-0.5, predicted=-0.4
>expected=3.0, predicted=2.8
>expected=2.9, predicted=2.6
>expected=3.0, predicted=2.5
>expected=-0.2, predicted=-0.3
>expected=-0.6, predicted=-0.6
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.2, predicted=-0.3
>expected=-0.2, predicted=-0.2
>expected=-0.5, predicted=-0.2
>expected=-0.5, predicted=-0.1
>expected=-0.2, predicted=-0.3
>expected=-0.1, predicted=-0.1
>expected=-0.7, predicted=-0.7
>expected=-0.5, predicted=-0.6
>expected=-0.5, predicted=-0.6
>expected=-0.6, predicted=-0.5
>expected=-0.6, predicted=-0.5
>expected=-0.6, predicted=-0.4
>expected=0.1, predicted=0.1
>expected=0.9, predicted=0.6
>expected=0.3, predicted=1.2
>expected=0.7, predicted=1.2
>expected=0.8, predicted=0.7
>expected=-0.3, predicted=-0.3
>expected=-0.5, predicted=-0.5
>expected=-0.6, predicted=-0.6
>expected=-0.5, predicted=-0.4
>expected=-0.5, predicted=-0.4
>expected=3.0, predicted=2.8
>expected=2.9, predicted=2.6
>expected=3.0, predicted=2.5
>expected=-0.2, predicted=-0.1
>expected=-0.6, predicted=-0.4
>expected=-0.7, predicted=-0.5
>expected=-0.7, predicted=-0.6
>expected=-0.7, predicted=-0.6
>expected=-0.7, predicted=-0.6
>expected=-0.7, predicted=-0.6
>expected=-0.2, predicted=-0.3
>expected=-0.2, predicted=-0.1
>expected=-0.5, predicted=-0.2
>expected=-0.5, predicted=-0.2
>expected=-0.2, predicted=-0.4
>expected=-0.1, predicted=-0.3
>expected=-0.7, predicted=-0.6
>expected=-0.5, predicted=-0.6
>expected=-0.5, predicted=-0.5
>expected=-0.6, predicted=-0.5
>expected=-0.6, predicted=-0.5
>expected=-0.6, predicted=-0.5
>expected=0.1, predicted=-0.0
>expected=0.9, predicted=1.0
>expected=0.3, predicted=0.8
>expected=0.7, predicted=0.8
>expected=0.8, predicted=1.0
>expected=-0.3, predicted=-0.2
>expected=-0.5, predicted=-0.5
>expected=-0.6, predicted=-0.6
>expected=-0.5, predicted=-0.4
>expected=-0.5, predicted=-0.4
>expected=3.0, predicted=2.5
>expected=2.9, predicted=2.7
>expected=3.0, predicted=2.5
>expected=-0.2, predicted=-0.3
>expected=-0.6, predicted=-0.6
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.2, predicted=-0.3
>expected=-0.2, predicted=-0.2
>expected=-0.5, predicted=0.0
>expected=-0.5, predicted=-0.2
>expected=-0.2, predicted=-0.4
>expected=-0.1, predicted=-0.2
>expected=-0.7, predicted=-0.7
>expected=-0.5, predicted=-0.6
>expected=-0.5, predicted=-0.6
>expected=-0.6, predicted=-0.5
>expected=-0.6, predicted=-0.4
>expected=-0.6, predicted=-0.4
>expected=0.1, predicted=0.1
>expected=0.9, predicted=0.8
>expected=0.3, predicted=0.9
>expected=0.7, predicted=1.0
>expected=0.8, predicted=0.9
>expected=-0.3, predicted=-0.3
>expected=-0.5, predicted=-0.5
>expected=-0.6, predicted=-0.6
>expected=-0.5, predicted=-0.5
>expected=-0.5, predicted=-0.4
>expected=3.0, predicted=2.3
>expected=2.9, predicted=2.7
>expected=3.0, predicted=2.7
>expected=-0.2, predicted=0.1
>expected=-0.6, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.2, predicted=-0.3
>expected=-0.2, predicted=-0.2
>expected=-0.5, predicted=-0.3
>expected=-0.5, predicted=-0.5
>expected=-0.2, predicted=-0.3
>expected=-0.1, predicted=-0.1
>expected=-0.7, predicted=-0.6
>expected=-0.5, predicted=-0.6
>expected=-0.5, predicted=-0.6
>expected=-0.6, predicted=-0.5
>expected=-0.6, predicted=-0.5
>expected=-0.6, predicted=-0.4
>expected=0.1, predicted=0.1
>expected=0.9, predicted=0.6
>expected=0.3, predicted=1.2
>expected=0.7, predicted=1.4
>expected=0.8, predicted=0.9
>expected=-0.3, predicted=-0.4
>expected=-0.5, predicted=-0.5
>expected=-0.6, predicted=-0.6
>expected=-0.5, predicted=-0.5
>expected=-0.5, predicted=-0.4
>expected=3.0, predicted=2.8
>expected=2.9, predicted=2.6
>expected=3.0, predicted=2.5
>expected=-0.2, predicted=-0.3
>expected=-0.6, predicted=-0.6
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.2, predicted=-0.3
>expected=-0.2, predicted=-0.2
>expected=-0.5, predicted=-0.2
>expected=-0.5, predicted=-0.1
>expected=-0.2, predicted=-0.3
>expected=-0.1, predicted=-0.1
>expected=-0.7, predicted=-0.7
>expected=-0.5, predicted=-0.6
>expected=-0.5, predicted=-0.6
>expected=-0.6, predicted=-0.5
>expected=-0.6, predicted=-0.5
>expected=-0.6, predicted=-0.4
>expected=0.1, predicted=0.1
>expected=0.9, predicted=0.6
>expected=0.3, predicted=1.2
>expected=0.7, predicted=1.2
>expected=0.8, predicted=0.7
>expected=-0.3, predicted=-0.3
>expected=-0.5, predicted=-0.5
>expected=-0.6, predicted=-0.6
>expected=-0.5, predicted=-0.4
>expected=-0.5, predicted=-0.4
>expected=3.0, predicted=2.8
>expected=2.9, predicted=2.6
>expected=3.0, predicted=2.5
>expected=-0.2, predicted=-0.1
>expected=-0.6, predicted=-0.4
>expected=-0.7, predicted=-0.5
>expected=-0.7, predicted=-0.6
>expected=-0.7, predicted=-0.6
>expected=-0.7, predicted=-0.6
>expected=-0.7, predicted=-0.6
>expected=-0.2, predicted=-0.3
>expected=-0.2, predicted=-0.1
>expected=-0.5, predicted=-0.2
>expected=-0.5, predicted=-0.2
>expected=-0.2, predicted=-0.4
>expected=-0.1, predicted=-0.3
>expected=-0.7, predicted=-0.6
>expected=-0.5, predicted=-0.6
>expected=-0.5, predicted=-0.5
>expected=-0.6, predicted=-0.5
>expected=-0.6, predicted=-0.5
>expected=-0.6, predicted=-0.5
>expected=0.1, predicted=-0.0
>expected=0.9, predicted=1.0
>expected=0.3, predicted=0.8
>expected=0.7, predicted=0.8
>expected=0.8, predicted=1.0
>expected=-0.3, predicted=-0.2
>expected=-0.5, predicted=-0.5
>expected=-0.6, predicted=-0.6
>expected=-0.5, predicted=-0.5
>expected=-0.5, predicted=-0.4
>expected=3.0, predicted=2.7
>expected=2.9, predicted=2.7
>expected=3.0, predicted=2.4
>expected=-0.2, predicted=-0.3
>expected=-0.6, predicted=-0.6
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.7, predicted=-0.7
>expected=-0.2, predicted=-0.3
>expected=-0.2, predicted=-0.2
>expected=-0.5, predicted=-0.1
>expected=-0.5, predicted=-0.2
>expected=-0.2, predicted=-0.4
>expected=-0.1, predicted=-0.2
>expected=-0.7, predicted=-0.7
>expected=-0.5, predicted=-0.6
>expected=-0.5, predicted=-0.6
>expected=-0.6, predicted=-0.5
>expected=-0.6, predicted=-0.5
>expected=-0.6, predicted=-0.4
>expected=0.1, predicted=0.2
>expected=0.9, predicted=1.1
>expected=0.3, predicted=1.0
>expected=0.7, predicted=0.9
>expected=0.8, predicted=0.8
>expected=-0.3, predicted=-0.3
>expected=-0.5, predicted=-0.5
No description has been provided for this image

EVALUATE THE MODEL¶

In [ ]:
# Create a DataFrame
metrics = {
    'Model': model_names,
    'MAE': mae_values,
    'RMSE': rmse_values,
    'R-squared': r2_values,
    'Nash-Sutcliffe Efficiency': nse_values,
    'Willmott\'s Index of Agreement': willmott_values
}

metrics = pd.DataFrame(metrics)
In [ ]:
metrics
Out[ ]:
Model MAE RMSE R-squared Nash-Sutcliffe Efficiency Willmott's Index of Agreement
0 LightGBM 0.147210 0.262236 0.935964 0.935964 0.982711
1 XGBoost 0.137944 0.233216 0.949353 0.949353 0.986443
2 SVM 0.142707 0.184150 0.968422 0.968422 0.991383
3 Random Forest 0.128732 0.208715 0.959436 0.959436 0.988968
In [ ]:
metrics = metrics.round(2)

fig, ax = plt.subplots(figsize=(20, 4))
ax.axis('off')

table = ax.table(cellText=metrics.values,
                 colLabels=metrics.columns,
                 cellLoc='center',
                 loc='center',
                 bbox=[0, 0, 1, 1])

table.auto_set_font_size(False)
table.set_fontsize(10)
table.scale(1.2, 1.2)

header_color = '#D0D0D0'
data_color = '#FFFFFF'

for i, key in enumerate(table._cells):
    cell = table._cells[key]
    cell.set_edgecolor('black')
    if key[0] == 0 or key[1] == -1:
        cell.set_text_props(weight='bold')
        cell.set_facecolor(header_color)
    else:
        cell.set_facecolor(data_color)

plt.title('Models Performance on Max Flow')
plt.show()
No description has been provided for this image
In [ ]:
colors = ['#27ad81', '#5dc863', '#aadc32', '#fde725']
bar_width = 0.4

# Metrics and Titles
metrics_title = {
    'MAE': 'Mean Absolute Error (MAE)',
    'RMSE': 'Root Mean Squared Error (RMSE)',
    'R-squared': 'R-squared',
    'Nash-Sutcliffe Efficiency': 'Nash-Sutcliffe Efficiency',
    'Willmott\'s Index of Agreement': 'Willmott\'s Index of Agreement'
}

# Plot each metric separately
for metric, title in metrics_title.items():
    fig, ax = plt.subplots(figsize=(8, 6))
    ax.bar(metrics['Model'], metrics[metric], color=colors, width=bar_width)
    # ax.set_title(title, fontsize=16)
    ax.set_ylabel(metric, fontsize=16)
    ax.tick_params(axis='x', rotation=30, labelsize=16)
    ax.tick_params(axis='y', labelsize=16)
    plt.tight_layout()
    plt.show()
No description has been provided for this image
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9. MIN FLOW ANALYSIS¶

In [ ]:
flow_min = transformed_data[transformed_data['Parameter']=='Min Flow']
In [ ]:
# drop the parameter columns
flow_min = flow_min.drop(columns=['Parameter'])
In [ ]:
flow_min.head()
Out[ ]:
Date Value
3 1995-01-01 0.212
8 1996-01-01 0.070
13 1997-01-01 0.169
18 1998-01-01 0.274
23 1999-01-01 0.116
In [ ]:
# sort according to  the date
flow_min = flow_min.sort_values(by='Date')
flow_min.head()
Out[ ]:
Date Value
3 1995-01-01 0.212
138 1995-02-01 0.223
273 1995-03-01 0.212
408 1995-04-01 0.200
543 1995-05-01 0.235
In [ ]:
flow_min.head()
Out[ ]:
Date Value
3 1995-01-01 0.212
138 1995-02-01 0.223
273 1995-03-01 0.212
408 1995-04-01 0.200
543 1995-05-01 0.235
In [ ]:
plt.figure(figsize=(20, 8))
flow_min.plot(x='Date', y='Value', kind='line', ax=plt.gca(), color='#8c564b', fontsize=12)
plt.xlabel('Date', fontdict={'fontsize':20})
plt.ylabel('Min Flow (m3/s)', fontdict={'fontsize':20})
plt.xticks(size = 20)
plt.yticks(size = 20)
plt.grid(linestyle='--')
plt.tight_layout()
plt.legend().remove()
plt.show()
No description has been provided for this image
In [ ]:
flow_min[flow_min.Value > 1]
Out[ ]:
Date Value
In [ ]:
# Add fuller test to check the stationarity of the dataset
def adfuller_test(values):
    result = adfuller(values)
    labels = ['ADF Test Statistic','p-value','#Lags Used', 'Number of Observations Used']
    for value, label in zip(result, labels):
        print(label+' : '+str(value))
    if result[1] <= 0.05:
        print("Strong evidence against the null hypothesis(H0)")
    else:
        print("Weak evidence against the null hypothesis(H0)")
In [ ]:
# H0: It is non stationary
# H1: It is stationary
In [ ]:
adfuller_test(flow_min['Value'])

ADF Test Statistic : -2.3097085744112578
p-value : 0.16885587943215408
#Lags Used : 13
Number of Observations Used : 310
Weak evidence against the null hypothesis(H0)
In [ ]:
flow_min = flow_min[['Date', 'Value']]
flow_min.set_index('Date', inplace=True)
flow_min.head()
Out[ ]:
Value
Date
1995-01-01 0.212
1995-02-01 0.223
1995-03-01 0.212
1995-04-01 0.200
1995-05-01 0.235
In [ ]:
flow_min_model_names = []
flow_min_mae_values = []
flow_min_rmse_values = []
flow_min_r2_values = []
flow_min_nse_values = []
flow_min_willmott_values = []

TRAIN THE MODEL¶

In [ ]:
# Assuming `flow min` is your time series DataFrame
series = flow_min
values = series.values
values = add_rolling_features(values, window=3)
values = pd.DataFrame(values).values
scaler = StandardScaler()
values = scaler.fit_transform(values)
data = series_to_supervised(values, n_in=6)
data_df = pd.DataFrame(data, index=series.index[6+2:])
In [ ]:
# Model names
models = [
    ('LightGBM', lightgbm_forecast),
    ('XGBoost', xgboost_forecast),
    ('SVM', svm_forecast),
    ('Random Forest', random_forest_forecast)
]

# Clear existing lists in case they contain previous values
model_names.clear()
mae_values.clear()
rmse_values.clear()
r2_values.clear()
nse_values.clear()
willmott_values.clear()

# Iterate over each model, perform walk-forward validation, and append metrics to lists
for model_name, model_func in models:
    mae, rmse, r2, nse, willmott, test_index, y, yhat = walk_forward_validation(data_df, model_func)
    
    model_names.append(model_name)
    mae_values.append(mae)
    rmse_values.append(rmse)
    r2_values.append(r2)
    nse_values.append(nse)
    willmott_values.append(willmott)

# Create a DataFrame
metrics = {
    'Model': model_names,
    'MAE': mae_values,
    'RMSE': rmse_values,
    'R-squared': r2_values,
    'Nash-Sutcliffe Efficiency': nse_values,
    'Willmott\'s Index of Agreement': willmott_values
}

metrics_df = pd.DataFrame(metrics)

# Plot the actual vs predicted values for each model
plt.figure(figsize=(16, 6))
plt.plot(test_index, y, label='Actual', linestyle='--', color='black', linewidth=2)



for model_name, model_func in models:
    _, _, _, _, _, test_index, _, yhat = walk_forward_validation(data_df, model_func)
    plt.plot(test_index, yhat, label=f'{model_name} Predicted', linestyle='--', color=colors_dict[model_name], linewidth=2)

plt.xlabel('Year and Month', fontsize=18)
plt.ylabel('Scaled Min Flow (m3/s)', fontsize=18)

plt.legend(fontsize=14, loc='upper right', bbox_to_anchor=(0.6, 1.15), ncol=1)

plt.xticks(rotation=45, fontsize=14)
plt.yticks(fontsize=14)

plt.grid(axis='y', linestyle='--')

ax = plt.gca()
ax.spines['top'].set_visible(False)
ax.spines['right'].set_visible(False)

plt.tight_layout()
plt.show()

>expected=-0.7, predicted=-0.5
>expected=-0.4, predicted=-0.5
>expected=0.0, predicted=0.5
>expected=0.3, predicted=0.7
>expected=-0.1, predicted=0.0
>expected=0.9, predicted=0.4
>expected=0.3, predicted=0.4
>expected=-0.3, predicted=-0.3
>expected=-0.1, predicted=-0.3
>expected=-0.2, predicted=-0.3
>expected=-0.7, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.7
>expected=-0.8, predicted=-0.7
>expected=1.1, predicted=0.5
>expected=1.4, predicted=0.8
>expected=1.0, predicted=0.9
>expected=1.3, predicted=0.5
>expected=-0.4, predicted=0.2
>expected=-0.5, predicted=-0.4
>expected=3.3, predicted=0.7
>expected=2.8, predicted=2.3
>expected=0.7, predicted=2.6
>expected=0.6, predicted=1.1
>expected=2.1, predicted=0.7
>expected=2.5, predicted=1.3
>expected=-0.1, predicted=-0.1
>expected=1.2, predicted=0.9
>expected=0.7, predicted=1.6
>expected=0.2, predicted=1.0
>expected=0.1, predicted=0.6
>expected=-0.3, predicted=0.0
>expected=-0.7, predicted=-0.4
>expected=-0.4, predicted=-0.5
>expected=0.0, predicted=0.0
>expected=0.3, predicted=0.6
>expected=-0.1, predicted=0.2
>expected=0.9, predicted=0.5
>expected=0.3, predicted=-0.2
>expected=-0.3, predicted=-0.4
>expected=-0.1, predicted=-0.2
>expected=-0.2, predicted=-0.3
>expected=-0.7, predicted=-0.7
>expected=-0.8, predicted=-0.7
>expected=-0.8, predicted=-0.7
>expected=-0.8, predicted=-0.7
>expected=1.1, predicted=0.8
>expected=1.4, predicted=1.5
>expected=1.0, predicted=0.7
>expected=1.3, predicted=1.0
>expected=-0.4, predicted=-0.2
>expected=-0.5, predicted=-0.4
>expected=3.3, predicted=1.1
>expected=2.8, predicted=2.3
>expected=0.7, predicted=2.9
>expected=0.6, predicted=0.3
>expected=2.1, predicted=1.0
>expected=2.5, predicted=0.4
>expected=-0.1, predicted=-0.3
>expected=1.2, predicted=0.8
>expected=0.7, predicted=0.4
>expected=0.2, predicted=0.2
>expected=0.1, predicted=0.8
>expected=-0.3, predicted=-0.3
>expected=-0.7, predicted=-0.5
>expected=-0.4, predicted=-0.3
>expected=0.0, predicted=0.1
>expected=0.3, predicted=0.5
>expected=-0.1, predicted=0.1
>expected=0.9, predicted=-0.1
>expected=0.3, predicted=0.1
>expected=-0.3, predicted=-0.7
>expected=-0.1, predicted=-0.4
>expected=-0.2, predicted=-0.6
>expected=-0.7, predicted=-0.7
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.7
>expected=-0.8, predicted=-0.7
>expected=1.1, predicted=0.5
>expected=1.4, predicted=1.2
>expected=1.0, predicted=0.1
>expected=1.3, predicted=0.7
>expected=-0.4, predicted=0.2
>expected=-0.5, predicted=-0.3
>expected=3.3, predicted=1.0
>expected=2.8, predicted=1.6
>expected=0.7, predicted=1.5
>expected=0.6, predicted=1.1
>expected=2.1, predicted=1.0
>expected=2.5, predicted=1.4
>expected=-0.1, predicted=0.2
>expected=1.2, predicted=-0.0
>expected=0.7, predicted=0.9
>expected=0.2, predicted=0.8
>expected=0.1, predicted=-0.0
>expected=-0.3, predicted=-0.2
>expected=-0.7, predicted=-0.3
>expected=-0.4, predicted=-0.4
>expected=0.0, predicted=0.0
>expected=0.3, predicted=0.3
>expected=-0.1, predicted=0.1
>expected=0.9, predicted=0.3
>expected=0.3, predicted=-0.1
>expected=-0.3, predicted=-0.2
>expected=-0.1, predicted=-0.3
>expected=-0.2, predicted=-0.3
>expected=-0.7, predicted=-0.6
>expected=-0.8, predicted=-0.7
>expected=-0.8, predicted=-0.7
>expected=-0.8, predicted=-0.8
>expected=1.1, predicted=0.6
>expected=1.4, predicted=0.9
>expected=1.0, predicted=0.8
>expected=1.3, predicted=0.9
>expected=-0.4, predicted=-0.1
>expected=-0.5, predicted=-0.5
>expected=3.3, predicted=0.9
>expected=2.8, predicted=3.0
>expected=0.7, predicted=3.1
>expected=0.6, predicted=2.0
>expected=2.1, predicted=1.0
>expected=2.5, predicted=1.3
>expected=-0.1, predicted=-0.1
>expected=1.2, predicted=1.2
>expected=0.7, predicted=1.1
>expected=0.2, predicted=0.6
>expected=0.1, predicted=0.9
>expected=-0.3, predicted=-0.1
>expected=-0.7, predicted=-0.5
>expected=-0.4, predicted=-0.5
>expected=0.0, predicted=0.5
>expected=0.3, predicted=0.7
>expected=-0.1, predicted=0.0
>expected=0.9, predicted=0.4
>expected=0.3, predicted=0.4
>expected=-0.3, predicted=-0.3
>expected=-0.1, predicted=-0.3
>expected=-0.2, predicted=-0.3
>expected=-0.7, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.7
>expected=-0.8, predicted=-0.7
>expected=1.1, predicted=0.5
>expected=1.4, predicted=0.8
>expected=1.0, predicted=0.9
>expected=1.3, predicted=0.5
>expected=-0.4, predicted=0.2
>expected=-0.5, predicted=-0.4
>expected=3.3, predicted=0.7
>expected=2.8, predicted=2.3
>expected=0.7, predicted=2.6
>expected=0.6, predicted=1.1
>expected=2.1, predicted=0.7
>expected=2.5, predicted=1.3
>expected=-0.1, predicted=-0.1
>expected=1.2, predicted=0.9
>expected=0.7, predicted=1.6
>expected=0.2, predicted=1.0
>expected=0.1, predicted=0.6
>expected=-0.3, predicted=0.0
>expected=-0.7, predicted=-0.4
>expected=-0.4, predicted=-0.5
>expected=0.0, predicted=0.0
>expected=0.3, predicted=0.6
>expected=-0.1, predicted=0.2
>expected=0.9, predicted=0.5
>expected=0.3, predicted=-0.2
>expected=-0.3, predicted=-0.4
>expected=-0.1, predicted=-0.2
>expected=-0.2, predicted=-0.3
>expected=-0.7, predicted=-0.7
>expected=-0.8, predicted=-0.7
>expected=-0.8, predicted=-0.7
>expected=-0.8, predicted=-0.7
>expected=1.1, predicted=0.8
>expected=1.4, predicted=1.5
>expected=1.0, predicted=0.7
>expected=1.3, predicted=1.0
>expected=-0.4, predicted=-0.2
>expected=-0.5, predicted=-0.4
>expected=3.3, predicted=1.1
>expected=2.8, predicted=2.3
>expected=0.7, predicted=2.9
>expected=0.6, predicted=0.3
>expected=2.1, predicted=1.0
>expected=2.5, predicted=0.4
>expected=-0.1, predicted=-0.3
>expected=1.2, predicted=0.8
>expected=0.7, predicted=0.4
>expected=0.2, predicted=0.2
>expected=0.1, predicted=0.8
>expected=-0.3, predicted=-0.3
>expected=-0.7, predicted=-0.5
>expected=-0.4, predicted=-0.3
>expected=0.0, predicted=0.1
>expected=0.3, predicted=0.5
>expected=-0.1, predicted=0.1
>expected=0.9, predicted=-0.1
>expected=0.3, predicted=0.1
>expected=-0.3, predicted=-0.7
>expected=-0.1, predicted=-0.4
>expected=-0.2, predicted=-0.6
>expected=-0.7, predicted=-0.7
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.7
>expected=-0.8, predicted=-0.7
>expected=1.1, predicted=0.5
>expected=1.4, predicted=1.2
>expected=1.0, predicted=0.1
>expected=1.3, predicted=0.7
>expected=-0.4, predicted=0.2
>expected=-0.5, predicted=-0.3
>expected=3.3, predicted=1.0
>expected=2.8, predicted=1.6
>expected=0.7, predicted=1.5
>expected=0.6, predicted=1.1
>expected=2.1, predicted=1.0
>expected=2.5, predicted=1.4
>expected=-0.1, predicted=0.2
>expected=1.2, predicted=-0.0
>expected=0.7, predicted=0.9
>expected=0.2, predicted=0.8
>expected=0.1, predicted=-0.0
>expected=-0.3, predicted=-0.2
>expected=-0.7, predicted=-0.4
>expected=-0.4, predicted=-0.2
>expected=0.0, predicted=-0.0
>expected=0.3, predicted=0.3
>expected=-0.1, predicted=-0.0
>expected=0.9, predicted=0.1
>expected=0.3, predicted=-0.0
>expected=-0.3, predicted=-0.2
>expected=-0.1, predicted=-0.3
>expected=-0.2, predicted=-0.3
>expected=-0.7, predicted=-0.6
>expected=-0.8, predicted=-0.7
>expected=-0.8, predicted=-0.7
>expected=-0.8, predicted=-0.8
>expected=1.1, predicted=0.6
>expected=1.4, predicted=0.9
>expected=1.0, predicted=0.4
>expected=1.3, predicted=0.6
>expected=-0.4, predicted=0.1
>expected=-0.5, predicted=-0.5
>expected=3.3, predicted=0.8
>expected=2.8, predicted=2.5
>expected=0.7, predicted=2.7
>expected=0.6, predicted=1.4
>expected=2.1, predicted=1.0
>expected=2.5, predicted=1.1
>expected=-0.1, predicted=0.1
>expected=1.2, predicted=0.9
>expected=0.7, predicted=1.2
>expected=0.2, predicted=0.4
>expected=0.1, predicted=0.7
>expected=-0.3, predicted=0.1
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EVALUATE THE MODEL¶

In [ ]:
# Create a DataFrame
metrics = {
    'Model': model_names,
    'MAE': mae_values,
    'RMSE': rmse_values,
    'R-squared': r2_values,
    'Nash-Sutcliffe Efficiency': nse_values,
    'Willmott\'s Index of Agreement': willmott_values
}
metrics = pd.DataFrame(metrics)
In [ ]:
metrics
Out[ ]:
Model MAE RMSE R-squared Nash-Sutcliffe Efficiency Willmott's Index of Agreement
0 LightGBM 0.510560 0.764473 0.494032 0.494032 0.814135
1 XGBoost 0.422930 0.735053 0.532226 0.532226 0.836220
2 SVM 0.500558 0.709194 0.564559 0.564559 0.831898
3 Random Forest 0.466310 0.770881 0.485514 0.485514 0.833792
In [ ]:
metrics = metrics.round(2)
fig, ax = plt.subplots(figsize=(20, 4))
ax.axis('off')

table = ax.table(cellText=metrics.values,
                 colLabels=metrics.columns,
                 cellLoc='center',
                 loc='center',
                 bbox=[0, 0, 1, 1])

table.auto_set_font_size(False)
table.set_fontsize(10)
table.scale(1.2, 1.2)

header_color = '#D0D0D0'
data_color = '#FFFFFF'

for i, key in enumerate(table._cells):
    cell = table._cells[key]
    cell.set_edgecolor('black')
    if key[0] == 0 or key[1] == -1:
        cell.set_text_props(weight='bold')
        cell.set_facecolor(header_color)
    else:
        cell.set_facecolor(data_color)

plt.title('Models Performance on Min Flow')
plt.show()
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In [ ]:
colors = ['#27ad81', '#5dc863', '#aadc32', '#fde725']
bar_width = 0.4

# Metrics and Titles
metrics_title = {
    'MAE': 'Mean Absolute Error (MAE)',
    'RMSE': 'Root Mean Squared Error (RMSE)',
    'R-squared': 'R-squared',
    'Nash-Sutcliffe Efficiency': 'Nash-Sutcliffe Efficiency',
    'Willmott\'s Index of Agreement': 'Willmott\'s Index of Agreement'
}

# Plot each metric separately
for metric, title in metrics_title.items():
    fig, ax = plt.subplots(figsize=(8, 6))
    ax.bar(metrics['Model'], metrics[metric], color=colors, width=bar_width)
    # ax.set_title(title, fontsize=16)
    ax.set_ylabel(metric, fontsize=16)
    ax.tick_params(axis='x', rotation=30, labelsize=16)
    ax.tick_params(axis='y', labelsize=16)
    plt.tight_layout()
    plt.show()
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10. RUNOFF (m3/s) ANALYSIS¶

In [ ]:
# Get the wind_min values
runoff = transformed_data[transformed_data['Parameter'] == parameters[4]]
runoff.head()
Out[ ]:
Parameter Date Value
4 Runoff 1995-01-01 1.658000
9 Runoff 1996-01-01 1.095387
14 Runoff 1997-01-01 1.856000
19 Runoff 1998-01-01 1.930000
24 Runoff 1999-01-01 9.392000
In [ ]:
# drop the parameter columns
runoff = runoff.drop(columns=['Parameter'])
In [ ]:
runoff.head()
Out[ ]:
Date Value
4 1995-01-01 1.658000
9 1996-01-01 1.095387
14 1997-01-01 1.856000
19 1998-01-01 1.930000
24 1999-01-01 9.392000
In [ ]:
# sort according to  the date
runoff = runoff.sort_values(by='Date')
runoff.head()
Out[ ]:
Date Value
4 1995-01-01 1.658
139 1995-02-01 1.158
274 1995-03-01 1.861
409 1995-04-01 1.554
544 1995-05-01 2.298
In [ ]:
runoff.head()
Out[ ]:
Date Value
4 1995-01-01 1.658
139 1995-02-01 1.158
274 1995-03-01 1.861
409 1995-04-01 1.554
544 1995-05-01 2.298
In [ ]:
plt.figure(figsize=(20, 8))
runoff.plot(x='Date', y='Value', kind='line', ax=plt.gca(), color='#ff7f0e', fontsize=12)
plt.xlabel('Date', fontdict={'fontsize':20})
plt.ylabel('Runoff (m3/s)', fontdict={'fontsize':20})
plt.xticks(size = 20)
plt.yticks(size = 20)
plt.grid(linestyle='--')
plt.tight_layout()
plt.legend().remove()
plt.show()
No description has been provided for this image
In [ ]:
# Add fuller test to check the stationarity of the dataset
def adfuller_test(values):
    result = adfuller(values)
    labels = ['ADF Test Statistic','p-value','#Lags Used', 'Number of Observations Used']
    for value, label in zip(result, labels):
        print(label+' : '+str(value))
    if result[1] <= 0.05:
        print("Strong evidence against the null hypothesis(H0)")
    else:
        print("Weak evidence against the null hypothesis(H0)")
In [ ]:
# H0: It is non stationary
# H1: It is stationary
In [ ]:
adfuller_test(runoff['Value'])

ADF Test Statistic : -4.186222397590971
p-value : 0.0006951911057647956
#Lags Used : 13
Number of Observations Used : 310
Strong evidence against the null hypothesis(H0)
In [ ]:
runoff = runoff[['Date', 'Value']]
runoff.set_index('Date', inplace=True)
runoff.head()
Out[ ]:
Value
Date
1995-01-01 1.658
1995-02-01 1.158
1995-03-01 1.861
1995-04-01 1.554
1995-05-01 2.298
In [ ]:
runoff_model_names = []
runoff_mae_values = []
runoff_rmse_values = []
runoff_r2_values = []
runoff_nse_values = []
runoff_willmott_values = []

TRAIN THE MODEL¶

In [ ]:
# Assuming `runoff` is your time series DataFrame
series = runoff
values = series.values
values = add_rolling_features(values, window=3)
values = pd.DataFrame(values).values
scaler = StandardScaler()
values = scaler.fit_transform(values)
data = series_to_supervised(values, n_in=6)
data_df = pd.DataFrame(data, index=series.index[6+2:])
In [ ]:
# Model names
models = [
    ('LightGBM', lightgbm_forecast),
    ('XGBoost', xgboost_forecast),
    ('SVM', svm_forecast),
    ('Random Forest', random_forest_forecast)
]

# Clear existing lists in case they contain previous values
model_names.clear()
mae_values.clear()
rmse_values.clear()
r2_values.clear()
nse_values.clear()
willmott_values.clear()

# Iterate over each model, perform walk-forward validation, and append metrics to lists
for model_name, model_func in models:
    mae, rmse, r2, nse, willmott, test_index, y, yhat = walk_forward_validation(data_df, model_func)
    
    model_names.append(model_name)
    mae_values.append(mae)
    rmse_values.append(rmse)
    r2_values.append(r2)
    nse_values.append(nse)
    willmott_values.append(willmott)

# Create a DataFrame
metrics = {
    'Model': model_names,
    'MAE': mae_values,
    'RMSE': rmse_values,
    'R-squared': r2_values,
    'Nash-Sutcliffe Efficiency': nse_values,
    'Willmott\'s Index of Agreement': willmott_values
}

metrics_df = pd.DataFrame(metrics)

# Plot the actual vs predicted values for each model
plt.figure(figsize=(16, 6))
plt.plot(test_index, y, label='Actual', linestyle='--', color='black', linewidth=2)



for model_name, model_func in models:
    _, _, _, _, _, test_index, _, yhat = walk_forward_validation(data_df, model_func)
    plt.plot(test_index, yhat, label=f'{model_name} Predicted', linestyle='--', color=colors_dict[model_name], linewidth=2)

plt.xlabel('Year and Month', fontsize=18)
plt.ylabel('Scaled Runoff (m3/s)', fontsize=18)

plt.legend(fontsize=14, loc='upper right', bbox_to_anchor=(0.6, 1.15), ncol=1)

plt.xticks(rotation=45, fontsize=14)
plt.yticks(fontsize=14)

plt.grid(axis='y', linestyle='--')

ax = plt.gca()
ax.spines['top'].set_visible(False)
ax.spines['right'].set_visible(False)

plt.tight_layout()
plt.show()

>expected=-0.5, predicted=-0.4
>expected=0.1, predicted=-0.0
>expected=0.6, predicted=0.7
>expected=0.4, predicted=-0.0
>expected=0.5, predicted=0.3
>expected=0.7, predicted=0.5
>expected=1.0, predicted=0.8
>expected=-0.6, predicted=-0.1
>expected=-0.2, predicted=-0.6
>expected=-0.3, predicted=-0.6
>expected=-0.9, predicted=-0.7
>expected=-0.9, predicted=-0.8
>expected=-0.9, predicted=-0.7
>expected=-0.9, predicted=-0.6
>expected=-0.8, predicted=-0.7
>expected=-0.8, predicted=-0.5
>expected=-0.8, predicted=-0.6
>expected=-0.8, predicted=-0.7
>expected=-0.8, predicted=-0.7
>expected=-0.9, predicted=-0.7
>expected=-0.6, predicted=-0.6
>expected=-0.6, predicted=-0.6
>expected=-0.8, predicted=-0.6
>expected=-0.8, predicted=-0.7
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.7
>expected=-0.5, predicted=-0.7
>expected=-0.3, predicted=-0.3
>expected=-0.4, predicted=-0.3
>expected=-0.4, predicted=-0.5
>expected=-0.8, predicted=-0.5
>expected=-0.7, predicted=-0.8
>expected=-0.5, predicted=-0.2
>expected=0.1, predicted=-0.1
>expected=0.6, predicted=0.6
>expected=0.4, predicted=0.0
>expected=0.5, predicted=0.2
>expected=0.7, predicted=0.5
>expected=1.0, predicted=0.5
>expected=-0.6, predicted=-0.4
>expected=-0.2, predicted=-0.5
>expected=-0.3, predicted=-0.3
>expected=-0.9, predicted=-0.5
>expected=-0.9, predicted=-0.6
>expected=-0.9, predicted=-0.9
>expected=-0.9, predicted=-0.8
>expected=-0.8, predicted=-0.6
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.9, predicted=-0.8
>expected=-0.6, predicted=-0.8
>expected=-0.6, predicted=-0.7
>expected=-0.8, predicted=-0.7
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.5, predicted=-0.6
>expected=-0.3, predicted=0.2
>expected=-0.4, predicted=-0.2
>expected=-0.4, predicted=-0.2
>expected=-0.8, predicted=-0.7
>expected=-0.7, predicted=-0.8
>expected=-0.5, predicted=-0.5
>expected=0.1, predicted=0.1
>expected=0.6, predicted=0.8
>expected=0.4, predicted=0.3
>expected=0.5, predicted=0.2
>expected=0.7, predicted=0.5
>expected=1.0, predicted=0.8
>expected=-0.6, predicted=-0.2
>expected=-0.2, predicted=-0.8
>expected=-0.3, predicted=-0.7
>expected=-0.9, predicted=-0.8
>expected=-0.9, predicted=-0.9
>expected=-0.9, predicted=-0.8
>expected=-0.9, predicted=-0.8
>expected=-0.8, predicted=-0.7
>expected=-0.8, predicted=-0.7
>expected=-0.8, predicted=-0.7
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.9, predicted=-0.8
>expected=-0.6, predicted=-0.6
>expected=-0.6, predicted=-0.7
>expected=-0.8, predicted=-0.7
>expected=-0.8, predicted=-0.7
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.5, predicted=-0.6
>expected=-0.3, predicted=-0.3
>expected=-0.4, predicted=-0.6
>expected=-0.4, predicted=-0.6
>expected=-0.8, predicted=-0.6
>expected=-0.7, predicted=-0.9
>expected=-0.5, predicted=-0.4
>expected=0.1, predicted=0.0
>expected=0.6, predicted=0.5
>expected=0.4, predicted=0.2
>expected=0.5, predicted=0.2
>expected=0.7, predicted=0.4
>expected=1.0, predicted=0.6
>expected=-0.6, predicted=-0.4
>expected=-0.2, predicted=-0.4
>expected=-0.3, predicted=-0.5
>expected=-0.9, predicted=-0.7
>expected=-0.9, predicted=-0.7
>expected=-0.9, predicted=-0.8
>expected=-0.9, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.9, predicted=-0.8
>expected=-0.6, predicted=-0.9
>expected=-0.6, predicted=-0.7
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.5, predicted=-0.6
>expected=-0.3, predicted=0.1
>expected=-0.4, predicted=-0.2
>expected=-0.4, predicted=-0.4
>expected=-0.8, predicted=-0.5
>expected=-0.7, predicted=-0.7
>expected=-0.5, predicted=-0.4
>expected=0.1, predicted=-0.0
>expected=0.6, predicted=0.7
>expected=0.4, predicted=-0.0
>expected=0.5, predicted=0.3
>expected=0.7, predicted=0.5
>expected=1.0, predicted=0.8
>expected=-0.6, predicted=-0.1
>expected=-0.2, predicted=-0.6
>expected=-0.3, predicted=-0.6
>expected=-0.9, predicted=-0.7
>expected=-0.9, predicted=-0.8
>expected=-0.9, predicted=-0.7
>expected=-0.9, predicted=-0.6
>expected=-0.8, predicted=-0.7
>expected=-0.8, predicted=-0.5
>expected=-0.8, predicted=-0.6
>expected=-0.8, predicted=-0.7
>expected=-0.8, predicted=-0.7
>expected=-0.9, predicted=-0.7
>expected=-0.6, predicted=-0.6
>expected=-0.6, predicted=-0.6
>expected=-0.8, predicted=-0.6
>expected=-0.8, predicted=-0.7
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.7
>expected=-0.5, predicted=-0.7
>expected=-0.3, predicted=-0.3
>expected=-0.4, predicted=-0.3
>expected=-0.4, predicted=-0.5
>expected=-0.8, predicted=-0.5
>expected=-0.7, predicted=-0.8
>expected=-0.5, predicted=-0.2
>expected=0.1, predicted=-0.1
>expected=0.6, predicted=0.6
>expected=0.4, predicted=0.0
>expected=0.5, predicted=0.2
>expected=0.7, predicted=0.5
>expected=1.0, predicted=0.5
>expected=-0.6, predicted=-0.4
>expected=-0.2, predicted=-0.5
>expected=-0.3, predicted=-0.3
>expected=-0.9, predicted=-0.5
>expected=-0.9, predicted=-0.6
>expected=-0.9, predicted=-0.9
>expected=-0.9, predicted=-0.8
>expected=-0.8, predicted=-0.6
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.9, predicted=-0.8
>expected=-0.6, predicted=-0.8
>expected=-0.6, predicted=-0.7
>expected=-0.8, predicted=-0.7
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.5, predicted=-0.6
>expected=-0.3, predicted=0.2
>expected=-0.4, predicted=-0.2
>expected=-0.4, predicted=-0.2
>expected=-0.8, predicted=-0.7
>expected=-0.7, predicted=-0.8
>expected=-0.5, predicted=-0.5
>expected=0.1, predicted=0.1
>expected=0.6, predicted=0.8
>expected=0.4, predicted=0.3
>expected=0.5, predicted=0.2
>expected=0.7, predicted=0.5
>expected=1.0, predicted=0.8
>expected=-0.6, predicted=-0.2
>expected=-0.2, predicted=-0.8
>expected=-0.3, predicted=-0.7
>expected=-0.9, predicted=-0.8
>expected=-0.9, predicted=-0.9
>expected=-0.9, predicted=-0.8
>expected=-0.9, predicted=-0.8
>expected=-0.8, predicted=-0.7
>expected=-0.8, predicted=-0.7
>expected=-0.8, predicted=-0.7
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.9, predicted=-0.8
>expected=-0.6, predicted=-0.6
>expected=-0.6, predicted=-0.7
>expected=-0.8, predicted=-0.7
>expected=-0.8, predicted=-0.7
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.5, predicted=-0.6
>expected=-0.3, predicted=-0.3
>expected=-0.4, predicted=-0.6
>expected=-0.4, predicted=-0.6
>expected=-0.8, predicted=-0.6
>expected=-0.7, predicted=-0.9
>expected=-0.5, predicted=-0.4
>expected=0.1, predicted=-0.1
>expected=0.6, predicted=0.5
>expected=0.4, predicted=0.1
>expected=0.5, predicted=0.1
>expected=0.7, predicted=0.5
>expected=1.0, predicted=0.7
>expected=-0.6, predicted=-0.3
>expected=-0.2, predicted=-0.4
>expected=-0.3, predicted=-0.5
>expected=-0.9, predicted=-0.7
>expected=-0.9, predicted=-0.7
>expected=-0.9, predicted=-0.8
>expected=-0.9, predicted=-0.8
>expected=-0.8, predicted=-0.7
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.9, predicted=-0.8
>expected=-0.6, predicted=-0.8
>expected=-0.6, predicted=-0.8
>expected=-0.8, predicted=-0.7
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.8, predicted=-0.8
>expected=-0.5, predicted=-0.6
>expected=-0.3, predicted=-0.0
>expected=-0.4, predicted=-0.3
>expected=-0.4, predicted=-0.3
>expected=-0.8, predicted=-0.5
>expected=-0.7, predicted=-0.7
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EVALUATE THE MODEL¶

In [ ]:
# Create a DataFrame
metrics = {
    'Model': model_names,
    'MAE': mae_values,
    'RMSE': rmse_values,
    'R-squared': r2_values,
    'Nash-Sutcliffe Efficiency': nse_values,
    'Willmott\'s Index of Agreement': willmott_values
}

metrics = pd.DataFrame(metrics)
In [ ]:
metrics
Out[ ]:
Model MAE RMSE R-squared Nash-Sutcliffe Efficiency Willmott's Index of Agreement
0 LightGBM 0.171717 0.204025 0.848730 0.848730 0.952940
1 XGBoost 0.156541 0.212774 0.835479 0.835479 0.949176
2 SVM 0.133483 0.184586 0.876182 0.876182 0.965221
3 Random Forest 0.131083 0.173587 0.890499 0.890499 0.966709
In [ ]:
metrics = metrics.round(2)

fig, ax = plt.subplots(figsize=(20, 4))
ax.axis('off')

table = ax.table(cellText=metrics.values,
                 colLabels=metrics.columns,
                 cellLoc='center',
                 loc='center',
                 bbox=[0, 0, 1, 1])

table.auto_set_font_size(False)
table.set_fontsize(10)
table.scale(1.2, 1.2)

header_color = '#D0D0D0'
data_color = '#FFFFFF'

for i, key in enumerate(table._cells):
    cell = table._cells[key]
    cell.set_edgecolor('black')
    if key[0] == 0 or key[1] == -1:
        cell.set_text_props(weight='bold')
        cell.set_facecolor(header_color)
    else:
        cell.set_facecolor(data_color)

plt.title('Models Performance on Runoff (m3/s)')
plt.show()
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In [ ]:
colors = ['#27ad81', '#5dc863', '#aadc32', '#fde725']
bar_width = 0.4

# Metrics and Titles
metrics_title = {
    'MAE': 'Mean Absolute Error (MAE)',
    'RMSE': 'Root Mean Squared Error (RMSE)',
    'R-squared': 'R-squared',
    'Nash-Sutcliffe Efficiency': 'Nash-Sutcliffe Efficiency',
    'Willmott\'s Index of Agreement': 'Willmott\'s Index of Agreement'
}

# Plot each metric separately
for metric, title in metrics_title.items():
    fig, ax = plt.subplots(figsize=(8, 6))
    ax.bar(metrics['Model'], metrics[metric], color=colors, width=bar_width)
    # ax.set_title(title, fontsize=16)
    ax.set_ylabel(metric, fontsize=16)
    ax.tick_params(axis='x', rotation=30, labelsize=16)
    ax.tick_params(axis='y', labelsize=16)
    plt.tight_layout()
    plt.show()
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The End¶